 2.2.1.1: On the real number line the origin is assigned the number ____. (p....
 2.2.4.1: To complete the square of x 2 + lOx , you would (addl subtract) the...
 2.2.2.1: Solve the equation 2(x + 3)  1 = 7. (pp. 8693)
 2.2.5.1: If x and y are two quantities, then y is directly proportional to x...
 2.1: In 16, find the following for each pair of points: (a) The distanc...
 2.2.3.1: The slope of a vertical line is ____ ; the slope of a horizontal li...
 2.2.1.2: If 3 and 5 are the coordinates of two points on the real number li...
 2.2.4.2: Use the Square Root Method to solve the equation (x  2)2 = 9. (pp....
 2.2.2.2: Solve the equation x2  9 = 0. (p. 8693)
 2.2.5.2: True or False If y varies directly with x, then y = '5:., where k ...
 2.2: In 16, find the following for each pair of points: (a) The distanc...
 2.2.3.2: For the line 2x + 3 y = 6, the xintercept is ____ and the yinterc...
 2.2.1.3: If 3 and 4 are the legs of a right triangle, the hypotenuse is ____...
 2.2.4.3: True or False Every equation of the form x 2 + i + ax + by + c = 0 ...
 2.2.2.3: The points, if any, at which a graph crosses or touches the coordin...
 2.2.5.3: In 314, write a general formula to describe each variation. y vari...
 2.3: In 16, find the following for each pair of points: (a) The distanc...
 2.2.3.3: A horizontal line is given by an equation of the form _____ where b...
 2.2.1.4: Use the converse of the Pythagorean Theorem to show that a triangle...
 2.2.4.4: For a circle, the __ is the distance from the center to any point o...
 2.2.2.4: The xintercepts of the graph of an equation are those xvalues for...
 2.2.5.4: In 314, write a general formula to describe each variation. v vari...
 2.4: In 16, find the following for each pair of points: (a) The distanc...
 2.2.3.4: True or False Vertical lines have an undefined slope.
 2.2.1.5: If (x, y) are the coordinates of a point P in the xyplane, then x ...
 2.2.4.5: True or False The radius of the circle x 2 + i = 9 is 3.
 2.2.2.5: If for every point (x, y) on the graph of an equation the point ( ...
 2.2.5.5: In 314, write a general formula to describe each variation. A vari...
 2.5: In 16, find the following for each pair of points: (a) The distanc...
 2.2.3.5: True or False The slope of the line 2y = 3x + 5 is 3.
 2.2.1.6: The coordinate axes divide the xyplane into four sections called _...
 2.2.4.6: True or False The center of the circle (x + 3 )2 + (y  2)2 = 13 is...
 2.2.2.6: If the graph of an equation is symmetric with respect to the yaxis ...
 2.2.5.6: In 314, write a general formula to describe each variation. V vari...
 2.6: In 16, find the following for each pair of points: (a) The distanc...
 2.2.3.6: True or False The point (1, 2) is on the line 2x + y = 4.
 2.2.1.7: If three distinct points P, Q, and R all lie on a line and if d(P, ...
 2.2.4.7: In 710, find the center and radius of each circle. Write the stand...
 2.2.2.7: If the graph of an equation is symmetric with respect to the origin...
 2.2.5.7: In 314, write a general formula to describe each variation. F vari...
 2.7: Graph y = x 2 + 4 by plotting points.
 2.2.3.7: Two nonvertical lines have slopes m[ and m2 , respectively. The lin...
 2.2.1.8: True or False The distance between two points is sometimes a negati...
 2.2.4.8: In 710, find the center and radius of each circle. Write the stand...
 2.2.2.8: True or False To find the yintercepts of the graph of an equation,...
 2.2.5.8: In 314, write a general formula to describe each variation. y vari...
 2.8: List the intercepts of the given graph. In 916, list the intercept...
 2.2.3.8: The lines y = 2x + 3 and y = ax + 5 are parallel if a= _____.
 2.2.1.9: True or False The point (1, 4) lies in quadrant IV of the Cartesia...
 2.2.4.9: In 710, find the center and radius of each circle. Write the stand...
 2.2.2.9: True or False The ycoordinate of a point at which the graph crosse...
 2.2.5.9: In 314, write a general formula to describe each variation. z vari...
 2.9: In 916, list the intercepts and test for symmetry with respect to ...
 2.2.3.9: The lines y = 2x  1 and y = ax + 2 are perpendicular if a= _____.
 2.2.1.10: True or False The midpoint of a line segment is found by averaging ...
 2.2.4.10: In 710, find the center and radius of each circle. Write the stand...
 2.2.2.10: True or False If a graph is symmetric with respect to the xaxis, t...
 2.2.5.10: In 314, write a general formula to describe each variation. T vari...
 2.10: In 916, list the intercepts and test for symmetry with respect to ...
 2.2.3.10: True or False Perpendicular lines have slopes that are reciprocals ...
 2.2.1.11: In 11 and 12, plot each point in the xyplane. Tell in which quadra...
 2.2.4.11: In 1120, write the standard form of the equation and the general f...
 2.2.2.11: In llI6, determine which of the given points are on the graph of t...
 2.2.5.11: In 314, write a general formula to describe each variation. M vari...
 2.11: In 916, list the intercepts and test for symmetry with respect to ...
 2.2.3.11: In 1114, (a) find the slope of the line and (b) interpret the slop...
 2.2.1.12: In 11 and 12, plot each point in the xyplane. Tell in which quadra...
 2.2.4.12: In 1120, write the standard form of the equation and the general f...
 2.2.2.12: In llI6, determine which of the given points are on the graph of t...
 2.2.5.12: In 314, write a general formula to describe each variation. z vari...
 2.12: In 916, list the intercepts and test for symmetry with respect to ...
 2.2.3.12: In 1114, (a) find the slope of the line and (b) interpret the slop...
 2.2.1.13: Plot the points (2, 0), (2, 3), (2, 4), (2, 1 ), and (2, 1). Desc...
 2.2.4.13: In 1120, write the standard form of the equation and the general f...
 2.2.2.13: In llI6, determine which of the given points are on the graph of t...
 2.2.5.13: In 314, write a general formula to describe each variation. The sq...
 2.13: In 916, list the intercepts and test for symmetry with respect to ...
 2.2.3.13: In 1114, (a) find the slope of the line and (b) interpret the slop...
 2.2.1.14: Plot the points (0, 3), (1, 3), ( 2, 3), (5, 3), and ( 4, 3). Des...
 2.2.4.14: In 1120, write the standard form of the equation and the general f...
 2.2.2.14: In llI6, determine which of the given points are on the graph of t...
 2.2.5.14: In 314, write a general formula to describe each variation. The cu...
 2.14: In 916, list the intercepts and test for symmetry with respect to ...
 2.2.3.14: In 1114, (a) find the slope of the line and (b) interpret the slop...
 2.2.1.15: In 1528, find the distance d(P] , P2) between the points PI and P2...
 2.2.4.15: In 1120, write the standard form of the equation and the general f...
 2.2.2.15: In llI6, determine which of the given points are on the graph of t...
 2.2.5.15: In 1520, write an equation that relates the quantities. Geometry T...
 2.15: In 916, list the intercepts and test for symmetry with respect to ...
 2.2.3.15: In 1522, plot each pair of points and determine the slope of the l...
 2.2.1.16: In 1528, find the distance d(P] , P2) between the points PI and P2...
 2.2.4.16: In 1120, write the standard form of the equation and the general f...
 2.2.2.16: In llI6, determine which of the given points are on the graph of t...
 2.2.5.16: In 1520, write an equation that relates the quantities. Geometry T...
 2.16: In 916, list the intercepts and test for symmetry with respect to ...
 2.2.3.16: In 1522, plot each pair of points and determine the slope of the l...
 2.2.1.17: In 1528, find the distance d(P] , P2) between the points PI and P2...
 2.2.4.17: In 1120, write the standard form of the equation and the general f...
 2.2.2.17: In 1728, find the intercepts and graph each equation by plotting p...
 2.2.5.17: In 1520, write an equation that relates the quantities. Geometry T...
 2.17: In 1720, find the standard form of the equation of the circle whos...
 2.2.3.17: In 1522, plot each pair of points and determine the slope of the l...
 2.2.1.18: In 1528, find the distance d(P] , P2) between the points PI and P2...
 2.2.4.18: In 1120, write the standard form of the equation and the general f...
 2.2.2.18: In 1728, find the intercepts and graph each equation by plotting p...
 2.2.5.18: In 1520, write an equation that relates the quantities. Geometry T...
 2.18: In 1720, find the standard form of the equation of the circle whos...
 2.2.3.18: In 1522, plot each pair of points and determine the slope of the l...
 2.2.1.19: In 1528, find the distance d(P] , P2) between the points PI and P2...
 2.2.4.19: In 1120, write the standard form of the equation and the general f...
 2.2.2.19: In 1728, find the intercepts and graph each equation by plotting p...
 2.2.5.19: In 1520, write an equation that relates the quantities. Physics: N...
 2.19: In 1720, find the standard form of the equation of the circle whos...
 2.2.3.19: In 1522, plot each pair of points and determine the slope of the l...
 2.2.1.20: In 1528, find the distance d(P] , P2) between the points PI and P2...
 2.2.4.20: In 1120, write the standard form of the equation and the general f...
 2.2.2.20: In 1728, find the intercepts and graph each equation by plotting p...
 2.2.5.20: In 1520, write an equation that relates the quantities. Physics: S...
 2.20: In 1720, find the standard form of the equation of the circle whos...
 2.2.3.20: In 1522, plot each pair of points and determine the slope of the l...
 2.2.1.21: In 1528, find the distance d(P] , P2) between the points PI and P2...
 2.2.4.21: In 2134, (a) find (he center (h, k) and radius r of each circle; (...
 2.2.2.21: In 1728, find the intercepts and graph each equation by plotting p...
 2.2.5.21: Mortgage Payments The monthly payment p on a mortgage varies direct...
 2.21: In 2126, find the center and radius of each circle. Graph each cir...
 2.2.3.21: In 1522, plot each pair of points and determine the slope of the l...
 2.2.1.22: In 1528, find the distance d(P] , P2) between the points PI and P2...
 2.2.4.22: In 2134, (a) find (he center (h, k) and radius r of each circle; (...
 2.2.2.22: In 1728, find the intercepts and graph each equation by plotting p...
 2.2.5.22: Mortgage Payments The monthly payment p on a mortgage varies direct...
 2.22: In 2126, find the center and radius of each circle. Graph each cir...
 2.2.3.22: In 1522, plot each pair of points and determine the slope of the l...
 2.2.1.23: In 1528, find the distance d(P] , P2) between the points PI and P2...
 2.2.4.23: In 2134, (a) find (he center (h, k) and radius r of each circle; (...
 2.2.2.23: In 1728, find the intercepts and graph each equation by plotting p...
 2.2.5.23: Physics: Falling Objects The distance s that an object falls is dir...
 2.23: In 2126, find the center and radius of each circle. Graph each cir...
 2.2.3.23: In 2330, graph the line containing the point P and having slope m....
 2.2.1.24: In 1528, find the distance d(P] , P2) between the points PI and P2...
 2.2.4.24: In 2134, (a) find (he center (h, k) and radius r of each circle; (...
 2.2.2.24: In 1728, find the intercepts and graph each equation by plotting p...
 2.2.5.24: Physics: Falling Objects The velocity v of a falling object is dire...
 2.24: In 2126, find the center and radius of each circle. Graph each cir...
 2.2.3.24: In 2330, graph the line containing the point P and having slope m....
 2.2.1.25: In 1528, find the distance d(P] , P2) between the points PI and P2...
 2.2.4.25: In 2134, (a) find (he center (h, k) and radius r of each circle; (...
 2.2.2.25: In 1728, find the intercepts and graph each equation by plotting p...
 2.2.5.25: Physics: Stretching a Spring The elongation E of a spring balance v...
 2.25: In 2126, find the center and radius of each circle. Graph each cir...
 2.2.3.25: In 2330, graph the line containing the point P and having slope m....
 2.2.1.26: In 1528, find the distance d(P] , P2) between the points PI and P2...
 2.2.4.26: In 2134, (a) find (he center (h, k) and radius r of each circle; (...
 2.2.2.26: In 1728, find the intercepts and graph each equation by plotting p...
 2.2.5.26: Physics: Vibrating String The rate of vibration of a string under c...
 2.26: In 2126, find the center and radius of each circle. Graph each cir...
 2.2.3.26: In 2330, graph the line containing the point P and having slope m....
 2.2.1.27: In 1528, find the distance d(P] , P2) between the points PI and P2...
 2.2.4.27: In 2134, (a) find (he center (h, k) and radius r of each circle; (...
 2.2.2.27: In 1728, find the intercepts and graph each equation by plotting p...
 2.2.5.27: Revenue Equation At the corner Shell station, the revenue R varies ...
 2.27: In 2736, find an equation of the line having the given characteris...
 2.2.3.27: In 2330, graph the line containing the point P and having slope m....
 2.2.1.28: In 1528, find the distance d(P] , P2) between the points PI and P2...
 2.2.4.28: In 2134, (a) find (he center (h, k) and radius r of each circle; (...
 2.2.2.28: In 1728, find the intercepts and graph each equation by plotting p...
 2.2.5.28: Cost Equation The cost C of chocolatecovered almonds varies direct...
 2.28: In 2736, find an equation of the line having the given characteris...
 2.2.3.28: In 2330, graph the line containing the point P and having slope m....
 2.2.1.29: In 2934, plot each point and form the triangle ABC. Verify that th...
 2.2.4.29: In 2134, (a) find (he center (h, k) and radius r of each circle; (...
 2.2.2.29: In 2938, plot each point. Then plot the point that is symmetric to...
 2.2.5.29: Demand Suppose that the demand D for candy at the movie theater is ...
 2.29: In 2736, find an equation of the line having the given characteris...
 2.2.3.29: In 2330, graph the line containing the point P and having slope m....
 2.2.1.30: In 2934, plot each point and form the triangle ABC. Verify that th...
 2.2.4.30: In 2134, (a) find (he center (h, k) and radius r of each circle; (...
 2.2.2.30: In 2938, plot each point. Then plot the point that is symmetric to...
 2.2.5.30: Driving to School The time t that it takes to get to school varies ...
 2.30: In 2736, find an equation of the line having the given characteris...
 2.2.3.30: In 2330, graph the line containing the point P and having slope m....
 2.2.1.31: In 2934, plot each point and form the triangle ABC. Verify that th...
 2.2.4.31: In 2134, (a) find (he center (h, k) and radius r of each circle; (...
 2.2.2.31: In 2938, plot each point. Then plot the point that is symmetric to...
 2.2.5.31: Pressure The volume of a gas V held at a constant temperature in a ...
 2.31: In 2736, find an equation of the line having the given characteris...
 2.2.3.31: In 3136, the slope and a point on a line are given. Use this infor...
 2.2.1.32: In 2934, plot each point and form the triangle ABC. Verify that th...
 2.2.4.32: In 2134, (a) find (he center (h, k) and radius r of each circle; (...
 2.2.2.32: In 2938, plot each point. Then plot the point that is symmetric to...
 2.2.5.32: Resistance The current i in a circuit is inversely proportional to ...
 2.32: In 2736, find an equation of the line having the given characteris...
 2.2.3.32: In 3136, the slope and a point on a line are given. Use this infor...
 2.2.1.33: In 2934, plot each point and form the triangle ABC. Verify that th...
 2.2.4.33: In 2134, (a) find (he center (h, k) and radius r of each circle; (...
 2.2.2.33: In 2938, plot each point. Then plot the point that is symmetric to...
 2.2.5.33: Weight The weight of an object above the surface of Earth varies in...
 2.33: In 2736, find an equation of the line having the given characteris...
 2.2.3.33: In 3136, the slope and a point on a line are given. Use this infor...
 2.2.3.34: In 3136, the slope and a point on a line are given. Use this infor...
 2.2.1.34: In 2934, plot each point and form the triangle ABC. Verify that th...
 2.2.4.34: In 2134, (a) find (he center (h, k) and radius r of each circle; (...
 2.2.2.34: In 2938, plot each point. Then plot the point that is symmetric to...
 2.2.5.34: Intensity of Light The intensity 1 of light (measured in footcandle...
 2.34: In 2736, find an equation of the line having the given characteris...
 2.2.3.35: In 3136, the slope and a point on a line are given. Use this infor...
 2.2.1.35: In 3544, find the midpoint of the line segment joining the points ...
 2.2.4.35: In 3542, find the standard form of the equation of each circle. Ce...
 2.2.2.35: In 2938, plot each point. Then plot the point that is symmetric to...
 2.2.5.35: Geometry The volume V of a right circular cylinder varies jointly w...
 2.35: In 2736, find an equation of the line having the given characteris...
 2.2.3.36: In 3136, the slope and a point on a line are given. Use this infor...
 2.2.1.36: In 3544, find the midpoint of the line segment joining the points ...
 2.2.4.36: In 3542, find the standard form of the equation of each circle. Ce...
 2.2.2.36: In 2938, plot each point. Then plot the point that is symmetric to...
 2.2.5.36: Geometry The volume V of a right circular cone varies jointly with ...
 2.36: In 2736, find an equation of the line having the given characteris...
 2.2.3.37: In 3744, jtnd an equation of the line L. 0;\.JL
 2.2.1.37: In 3544, find the midpoint of the line segment joining the points ...
 2.2.4.37: In 3542, find the standard form of the equation of each circle. Ce...
 2.2.2.37: In 2938, plot each point. Then plot the point that is symmetric to...
 2.2.5.37: Weight of a Body The weight of a body above the surface of Earth va...
 2.37: In 3 740, find the slope and yintercept of each line. Graph the l...
 2.2.3.38: In 3744, jtnd an equation of the line L. Y(2,1) 2(0,0)
 2.2.1.38: In 3544, find the midpoint of the line segment joining the points ...
 2.2.4.38: In 3542, find the standard form of the equation of each circle. Ce...
 2.2.2.38: In 2938, plot each point. Then plot the point that is symmetric to...
 2.2.5.38: Force of the Wind on a Window The force exerted by the wind on a pl...
 2.38: In 3 740, find the slope and yintercept of each line. Graph the l...
 2.39: In 3 740, find the slope and yintercept of each line. Graph the l...
 2.2.3.39: In 3744, jtnd an equation of the line L. (1,3) 3 (1,1)1 L'"
 2.2.1.39: In 3544, find the midpoint of the line segment joining the points ...
 2.2.4.39: In 3542, find the standard form of the equation of each circle. Wi...
 2.2.2.39: In 3950, the graph of an equation is given. (a) Find the intercept...
 2.2.5.39: Horsepower The horsepower (hp) that a shaft can safely transmit var...
 2.40: In 3 740, find the slope and yintercept of each line. Graph the l...
 2.2.3.40: In 3744, jtnd an equation of the line L. Y (2,2) _L2 2
 2.2.1.40: In 3544, find the midpoint of the line segment joining the points ...
 2.2.4.40: In 3542, find the standard form of the equation of each circle. Wi...
 2.2.2.40: In 3950, the graph of an equation is given. (a) Find the intercept...
 2.2.5.40: Chemistry: Gas Laws The volume V of an ideal gas varies directly wi...
 2.41: In 4144, find the intercepts and graph each line. 2x  3y = 12
 2.2.3.41: In 3744, jtnd an equation of the line L. y=2x 3a 10;\.JL.JL is pa...
 2.2.1.41: In 3544, find the midpoint of the line segment joining the points ...
 2.2.4.41: In 3542, find the standard form of the equation of each circle. Ce...
 2.2.2.41: In 3950, the graph of an equation is given. (a) Find the intercept...
 2.2.5.41: Physics: Kinetic Energy The kinetic energy K of a moving object var...
 2.42: In 4144, find the intercepts and graph each line. x  2y = 8
 2.2.3.42: In 3744, jtnd an equation of the line L. L is parallel to y =x
 2.2.1.42: In 3544, find the midpoint of the line segment joining the points ...
 2.2.4.42: In 3542, find the standard form of the equation of each circle. Ce...
 2.2.2.42: In 3950, the graph of an equation is given. (a) Find the intercept...
 2.2.5.42: Electrical Resistance of a Wire The electrical resistance of a wire...
 2.43: In 4144, find the intercepts and graph each line. 1 1 43 , + y = 2
 2.2.3.43: In 3744, jtnd an equation of the line L. y= 2xL is perpendicularto...
 2.2.1.43: In 3544, find the midpoint of the line segment joining the points ...
 2.2.4.43: In 4346, match each graph with the correct equation. (a) (x  3)2 ...
 2.2.2.43: In 3950, the graph of an equation is given. (a) Find the intercept...
 2.2.5.43: Measuring the Stress of Materials The stress in the material of a p...
 2.44: In 4144, find the intercepts and graph each line. 1 x 1 = 1 3x
 2.2.3.44: In 3744, jtnd an equation of the line L. y=xL is perpendicularto ...
 2.2.1.44: In 3544, find the midpoint of the line segment joining the points ...
 2.2.4.44: In 4346, match each graph with the correct equation. (a) (x  3)2 ...
 2.2.2.44: In 3950, the graph of an equation is given. (a) Find the intercept...
 2.2.5.44: Safe Load for a Beam The maximum safe load for a horizontal rectang...
 2.45: Sketch a graph of y = x3.
 2.2.3.45: In 4570, find an equation for the line with the given properties. ...
 2.2.1.45: Find all points having an xcoordinate of 2 whose distance from the...
 2.2.4.45: In 4346, match each graph with the correct equation. (a) (x  3)2 ...
 2.2.2.45: In 3950, the graph of an equation is given. (a) Find the intercept...
 2.2.5.45: In the early 17th century, Johannes Kepler discovered that the squa...
 2.46: Sketch a graph of y = Yx.
 2.2.3.46: In 4570, find an equation for the line with the given properties. ...
 2.2.1.46: Find all points having a ycoordinate of 3 whose distance from the...
 2.2.4.46: In 4346, match each graph with the correct equation. (a) (x  3)2 ...
 2.2.2.46: In 3950, the graph of an equation is given. (a) Find the intercept...
 2.2.5.46: Using a situation that has not been discussed in the text, write a ...
 2.47: Graph the line with slope '3 containing the point (1, 2).
 2.2.3.47: In 4570, find an equation for the line with the given properties. ...
 2.2.1.47: Find all points on the xaxis that are 5 units from the point (4, 3).
 2.2.4.47: Find the area of the square in the figure. x
 2.2.2.47: In 3950, the graph of an equation is given. (a) Find the intercept...
 2.2.5.47: Using a situation that has not been discussed in the text, write a ...
 2.48: Show that the points A = (3, 4), B = (1, 1), and C = ( 2, 3) are t...
 2.2.3.48: In 4570, find an equation for the line with the given properties. ...
 2.2.1.48: Find all points on the yaxis that are 5 units from the point (4, 4).
 2.2.4.48: Find the area of the shaded region in the figure assuming the quadr...
 2.2.2.48: In 3950, the graph of an equation is given. (a) Find the intercept...
 2.2.5.48: Using a situation that has not been discussed in the text, write a ...
 2.49: Show that the points A = ( 2, 0), B = ( 4, 4), and C = (8, 5) are...
 2.2.3.49: In 4570, find an equation for the line with the given properties. ...
 2.2.1.49: The midpoint of the line segment from Pi ta P2 is (1, 4). If p] = ...
 2.2.4.49: Ferris Wheel The original Ferris wheel was built in 1893 by Pittsbu...
 2.2.2.49: In 3950, the graph of an equation is given. (a) Find the intercept...
 2.50: The endpoints of the diameter of a circle are ( 3, 2) and (5, 6)....
 2.2.3.50: In 4570, find an equation for the line with the given properties. ...
 2.2.1.50: The midpoint of the line segment from PI to P2 is (5, 4). If P2 = ...
 2.2.4.50: Ferris Wheel In 2006, the star of Nanchang (in the Jiangxi province...
 2.2.2.50: In 3950, the graph of an equation is given. (a) Find the intercept...
 2.51: Show that the points A = (2, 5), B = (6, 1), and C = (8, 1) lie on...
 2.2.3.51: In 4570, find an equation for the line with the given properties. ...
 2.2.1.51: Geometry The medians of a triangle are the line segments from each ...
 2.2.4.51: Weather Satellites Earth is represented on a map of a portion of th...
 2.2.2.51: In 5154, draw a complete graph so that it has the type of symmetry...
 2.52: Mortgage Payments The monthly payment p on a mortgage varies direct...
 2.2.3.52: In 4570, find an equation for the line with the given properties. ...
 2.2.1.52: Geometry An equilateral triangle is one in which all three sides ar...
 2.2.4.52: The tangent line to a circle may be defined as the line that inters...
 2.2.2.52: In 5154, draw a complete graph so that it has the type of symmetry...
 2.53: Revenue Function At the corner Esso station, the revenue R varies d...
 2.2.3.53: In 4570, find an equation for the line with the given properties. ...
 2.2.1.53: Geometry Find the midpoint of each diagonal of a square with side o...
 2.2.4.53: The Greek Method The Greek method for finding the equation of the t...
 2.2.2.53: In 5154, draw a complete graph so that it has the type of symmetry...
 2.54: Weight of a Body The weight of a body varies inversely with the squ...
 2.2.3.54: In 4570, find an equation for the line with the given properties. ...
 2.2.1.54: Geometry Verify that the points (0, 0), (a, 0), and (%' V; a ) are ...
 2.2.4.54: Use the Greek method described in to find an equation of the tangen...
 2.2.2.54: In 5154, draw a complete graph so that it has the type of symmetry...
 2.55: Kepler's Third Law of Planetary Motion Kepler's Third Law of Planet...
 2.2.3.55: In 4570, find an equation for the line with the given properties. ...
 2.2.1.55: In 5558, find the length of each side of the triangle determined b...
 2.2.4.55: Refer to 52. The line x  2y + 4 = 0 is tangent to a circle at (0, ...
 2.2.2.55: In 5570, list the intercepts and test for symmetry. / = x + 4
 2.56: Create four problems that you might be asked to do given the two po...
 2.2.3.56: In 4570, find an equation for the line with the given properties. ...
 2.2.1.56: In 5558, find the length of each side of the triangle determined b...
 2.2.4.56: Find an equation of the line containing the centers of the two circ...
 2.2.2.56: In 5570, list the intercepts and test for symmetry. / = x + 9
 2.57: Describe each of the following graphs in the xyplane. Give justifi...
 2.2.3.57: In 4570, find an equation for the line with the given properties. ...
 2.2.1.57: In 5558, find the length of each side of the triangle determined b...
 2.2.4.57: If a circle of radius 2 is made to roll along the xaxis, what is a...
 2.2.2.57: In 5570, list the intercepts and test for symmetry. y = 0X
 2.58: Suppose that you have a rectangular field that requires watering. Y...
 2.2.3.58: In 4570, find an equation for the line with the given properties. ...
 2.2.1.58: In 5558, find the length of each side of the triangle determined b...
 2.2.4.58: If the circumference of a circle is 67T, what is its radius?
 2.2.2.58: In 5570, list the intercepts and test for symmetry. y = 0'X
 2.2.3.59: In 4570, find an equation for the line with the given properties. ...
 2.2.1.59: Baseball A major league baseball "diamond" is actually a square, 90...
 2.2.4.59: Which of the following equations might have the graph shown? (More ...
 2.2.2.59: In 5570, list the intercepts and test for symmetry. x2 + y  9 = 0
 2.2.3.60: In 4570, find an equation for the line with the given properties. ...
 2.2.1.60: Little League Baseball The layout of a Little League playing field ...
 2.2.4.60: Which of the following equations might have the graph shown? (More ...
 2.2.2.60: In 5570, list the intercepts and test for symmetry. x2  Y  4 = 0
 2.2.3.61: In 4570, find an equation for the line with the given properties. ...
 2.2.1.61: Baseball Refer to 59. Overlay a rectangular coordinate system on a ...
 2.2.4.61: Explain how the center and radius of a circle can be used to graph ...
 2.2.2.61: In 5570, list the intercepts and test for symmetry. 9x2 + 4/ = 36
 2.2.3.62: In 4570, find an equation for the line with the given properties. ...
 2.2.1.62: Little League Baseball Refer to 60. Overlay a rectangular coordinat...
 2.2.2.62: In 5570, list the intercepts and test for symmetry. 4x2 + / = 4
 2.2.3.63: In 4570, find an equation for the line with the given properties. ...
 2.2.1.63: Distance between Moving Objects A Dodge Neon and a Mack truck leave...
 2.2.2.63: In 5570, list the intercepts and test for symmetry. Y = x3  27
 2.2.3.64: In 4570, find an equation for the line with the given properties. ...
 2.2.1.64: Distance of a Moving Object from a Fixed Point A hotair balloon, h...
 2.2.2.64: In 5570, list the intercepts and test for symmetry. Y = X4  1
 2.2.3.65: In 4570, find an equation for the line with the given properties. ...
 2.2.1.65: Drafting Error When a draftsman draws three lines that are to inter...
 2.2.2.65: In 5570, list the intercepts and test for symmetry. Y = x2  3x  4
 2.2.3.66: In 4570, find an equation for the line with the given properties. ...
 2.2.1.66: Net Sa les The figure illustrates how net sales of WalMart Stores,...
 2.2.2.66: In 5570, list the intercepts and test for symmetry. y = x2 + 4
 2.2.3.67: In 4570, find an equation for the line with the given properties. ...
 2.2.2.67: In 5570, list the intercepts and test for symmetry. Y =x2 + 9
 2.2.3.68: In 4570, find an equation for the line with the given properties. ...
 2.2.2.68: In 5570, list the intercepts and test for symmetry. y = 2
 2.2.3.69: In 4570, find an equation for the line with the given properties. ...
 2.2.2.69: In 5570, list the intercepts and test for symmetry. y =x2 _ 9
 2.2.3.70: In 4570, find an equation for the line with the given properties. ...
 2.2.2.70: In 5570, list the intercepts and test for symmetry. Y =X4 + 12x5
 2.2.3.71: In 7190, find the slope and yintercept of each line. Graph the li...
 2.2.2.71: In 7174, draw a quick sketch of each equation. y=x3
 2.2.3.72: In 7190, find the slope and yintercept of each line. Graph the li...
 2.2.2.72: In 7174, draw a quick sketch of each equation. x =/
 2.2.3.73: In 7190, find the slope and yintercept of each line. Graph the li...
 2.2.2.73: In 7174, draw a quick sketch of each equation. Y = Vx
 2.2.3.74: In 7190, find the slope and yintercept of each line. Graph the li...
 2.2.2.74: In 7174, draw a quick sketch of each equation. Y =
 2.2.3.75: In 7190, find the slope and yintercept of each line. Graph the li...
 2.2.2.75: If (3, b) is a point on the graph of y = 4x + 1, what is b?
 2.2.3.76: In 7190, find the slope and yintercept of each line. Graph the li...
 2.2.2.76: If ( 2, b) is a point on the graph of 2x + 3 y = 2, what is b?
 2.2.3.77: In 7190, find the slope and yintercept of each line. Graph the li...
 2.2.2.77: If ( a, 4) is a point on the graph of y = x 2 + 3x, what is a?
 2.2.3.78: In 7190, find the slope and yintercept of each line. Graph the li...
 2.2.2.78: If (a, 5) is a point on the graph of y = x2 + 6x, what is a?
 2.2.3.79: In 7190, find the slope and yintercept of each line. Graph the li...
 2.2.2.79: Given that the point (1,2) is on the graph of an equation that is s...
 2.2.3.80: In 7190, find the slope and yintercept of each line. Graph the li...
 2.2.2.80: If the graph of an equation is symmetric with respect to the yaxis...
 2.2.3.81: In 7190, find the slope and yintercept of each line. Graph the li...
 2.2.2.81: If the graph of an equation is symmetric with respect to the origin...
 2.2.3.82: In 7190, find the slope and yintercept of each line. Graph the li...
 2.2.2.82: If the graph of an equation is symmetric with respect to the xaxis...
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 2.2.2.83: Micro phones In studios and on stages, cardioid microphones are oft...
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 2.2.2.84: Solar Energy The solar electric generating systems at Kramer Juncti...
 2.2.3.85: In 7190, find the slope and yintercept of each line. Graph the li...
 2.2.2.85: In 85, you m ay use a graphing utility, but it is not required. (a)...
 2.2.3.86: In 7190, find the slope and yintercept of each line. Graph the li...
 2.2.2.86: Explain what is meant by a complete graph.
 2.2.3.87: In 7190, find the slope and yintercept of each line. Graph the li...
 2.2.2.87: Draw a graph of an equation that contains two xintercepts; at one ...
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 2.2.2.88: Make up an equation with the intercepts (2, 0), (4, 0), and (0, 1 )...
 2.2.3.89: In 7190, find the slope and yintercept of each line. Graph the li...
 2.2.2.89: Draw a graph that contains the points ( 2, 1), (0, 1 ), (1, 3), a...
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 2.2.2.90: An equation is being tested for symmetry with respect to the xaxis...
 2.2.3.91: In 91100, (a) find the intercepts of the graph of each equation an...
 2.2.3.92: In 91100, (a) find the intercepts of the graph of each equation an...
 2.2.3.93: In 91100, (a) find the intercepts of the graph of each equation an...
 2.2.3.94: In 91100, (a) find the intercepts of the graph of each equation an...
 2.2.3.95: In 91100, (a) find the intercepts of the graph of each equation an...
 2.2.3.96: In 91100, (a) find the intercepts of the graph of each equation an...
 2.2.3.97: In 91100, (a) find the intercepts of the graph of each equation an...
 2.2.3.98: In 91100, (a) find the intercepts of the graph of each equation an...
 2.2.3.99: In 91100, (a) find the intercepts of the graph of each equation an...
 2.2.3.100: In 91100, (a) find the intercepts of the graph of each equation an...
 2.2.3.101: Find an equation of the xaxis.
 2.2.3.102: Find an equation of the yaxis.
 2.2.3.103: In 103106, the equations of two lines are given. Determine if the ...
 2.2.3.104: In 103106, the equations of two lines are given. Determine if the ...
 2.2.3.105: In 103106, the equations of two lines are given. Determine if the ...
 2.2.3.106: In 103106, the equations of two lines are given. Determine if the ...
 2.2.3.107: In 107110, write an equation of each line. Express your answer usi...
 2.2.3.108: In 107110, write an equation of each line. Express your answer usi...
 2.2.3.109: In 107110, write an equation of each line. Express your answer usi...
 2.2.3.110: In 107110, write an equation of each line. Express your answer usi...
 2.2.3.111: Geometry Use slopes to show that the triangle whose vertices are (...
 2.2.3.112: Geometry Use slopes to show that the quadrilateral whose vertices a...
 2.2.3.113: Geometry Use slopes to show that the quadrilateral whose vertices a...
 2.2.3.114: Geometry Use slopes and the distance formula to show that the quadr...
 2.2.3.115: Truck Rentals A truck rental company rents a moving truck for one d...
 2.2.3.116: Cost Equation The fixed costs of operating a business are the costs...
 2.2.3.117: Cost of Sunday Home Delivery The cost to the Chicago Tribune for Su...
 2.2.3.118: Wages of a Car Salesperson Dan receives $375 per week for selling n...
 2.2.3.119: Electricity Rates in Illinois Commonwealth Edison Company supplies ...
 2.2.3.120: Electricity Rates in Florida Florida Power & Light Company supplies...
 2.2.3.121: Measuring Temperature The relationship between Celsius (0C) and Fah...
 2.2.3.122: Measuring Temperature The Kelvin (K) scale for measuring temperatur...
 2.2.3.123: Access Ramp A wooden access ramp is being built to reach a platform...
 2.2.3.124: Cigarette Use A study by the Partnership for a DrugFree America in...
 2.2.3.125: Product Promotion A cereal company finds that the number of people ...
 2.2.3.126: Show that the line containing the points (a, b) and (b, a), a "* b,...
 2.2.3.127: The equation 2x  y = C defines a family of lines, one line for eac...
 2.2.3.128: Prove that if two non vertical lines have slopes whose product is ...
 2.2.3.129: Which of the following equations might have the graph shown? (More ...
 2.2.3.130: Which of the following equations might h ave the graph shown? (More...
 2.2.3.131: The figure shows the graph of two parallel lines. Which of the foll...
 2.2.3.132: The figure shows the graph of two perpendicular lines. Which of the...
 2.2.3.133: m is for Slope The accepted symbol used to denote the slope of a li...
 2.2.3.134: Grade of a Road The term grade is used to describe the inclination ...
 2.2.3.135: Carpentry Carpenters use the term pitch to describe the steepness o...
 2.2.3.136: Can the equation of every line be written in slopeintercept form? ...
 2.2.3.137: Does every line have exactly one xintercept and one yintercept? A...
 2.2.3.138: What can you say about two lines that have equal slopes and equal y...
 2.2.3.139: What can you say about two lines with the same xintercept and the ...
 2.2.3.140: If two distinct lines have the same slope, but different xintercept...
 2.2.3.141: If two distinct lines have the same yintercept, but different slop...
 2.2.3.142: Which form of the equation of a line do you prefer to use? Justify ...
Solutions for Chapter 2: Graphs
Full solutions for Algebra and Trigonometry  8th Edition
ISBN: 9780132329033
Solutions for Chapter 2: Graphs
Get Full SolutionsAlgebra and Trigonometry was written by and is associated to the ISBN: 9780132329033. This textbook survival guide was created for the textbook: Algebra and Trigonometry, edition: 8. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 2: Graphs includes 465 full stepbystep solutions. Since 465 problems in chapter 2: Graphs have been answered, more than 59596 students have viewed full stepbystep solutions from this chapter.

Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.

Augmented matrix [A b].
Ax = b is solvable when b is in the column space of A; then [A b] has the same rank as A. Elimination on [A b] keeps equations correct.

Basis for V.
Independent vectors VI, ... , v d whose linear combinations give each vector in V as v = CIVI + ... + CdVd. V has many bases, each basis gives unique c's. A vector space has many bases!

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

Free variable Xi.
Column i has no pivot in elimination. We can give the n  r free variables any values, then Ax = b determines the r pivot variables (if solvable!).

Full row rank r = m.
Independent rows, at least one solution to Ax = b, column space is all of Rm. Full rank means full column rank or full row rank.

Jordan form 1 = M 1 AM.
If A has s independent eigenvectors, its "generalized" eigenvector matrix M gives 1 = diag(lt, ... , 1s). The block his Akh +Nk where Nk has 1 's on diagonall. Each block has one eigenvalue Ak and one eigenvector.

Krylov subspace Kj(A, b).
The subspace spanned by b, Ab, ... , AjIb. Numerical methods approximate A I b by x j with residual b  Ax j in this subspace. A good basis for K j requires only multiplication by A at each step.

Left inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

Linear transformation T.
Each vector V in the input space transforms to T (v) in the output space, and linearity requires T(cv + dw) = c T(v) + d T(w). Examples: Matrix multiplication A v, differentiation and integration in function space.

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

Row picture of Ax = b.
Each equation gives a plane in Rn; the planes intersect at x.

Simplex method for linear programming.
The minimum cost vector x * is found by moving from comer to lower cost comer along the edges of the feasible set (where the constraints Ax = b and x > 0 are satisfied). Minimum cost at a comer!

Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.