 2.5.1: The pointslope form of the equation of a nonvertical line with slo...
 2.5.2: Two parallel lines have ______________ slopes.
 2.5.3: The product of the slopes of two nonvertical perpendicular lines is...
 2.5.4: The negative reciprocal of 5 is ______________.
 2.5.5: The negative reciprocal of  3 5 is ______________.
 2.5.6: The slope of the line whose equation is y = 4x + 3 is _____________...
 2.5.7: The slope of the line whose equation is y = 1 2 x  5 is __________...
 2.5.8: Slope = 4, passing through (0, 3)
 2.5.9: Slope = 1, passing through 12,  1 2 2
 2.5.10: Slope = 1, passing through 1 1 4 , 42
 2.5.11: Slope = 1 4 , passing through the origin
 2.5.12: Slope = 1 5 , passing through the origin
 2.5.13: Slope =  2 3 , passing through (6, 4)
 2.5.14: Slope =  2 5 , passing through (15, 4)
 2.5.15: Passing through (6, 3) and (5, 2)
 2.5.16: Passing through (1, 3) and (2, 4)
 2.5.17: Passing through (2, 0) and (0, 4)
 2.5.18: Passing through (2, 0) and (0, 1)
 2.5.19: Passing through (6, 13) and (2, 5)
 2.5.20: Passing through (3, 2) and (2, 8)
 2.5.21: Passing through (1, 9) and (4, 2)
 2.5.22: Passing through (4, 8) and (8, 3)
 2.5.23: Passing through (2, 5) and (3, 5)
 2.5.24: Passing through (1, 4) and (3, 4)
 2.5.25: Passing through (7, 8) with xintercept = 3
 2.5.26: Passing through (4, 5) with yintercept = 3
 2.5.27: xintercept = 2 and yintercept = 1
 2.5.28: xintercept = 2 and yintercept = 4
 2.5.29: y = 5x
 2.5.30: y = 3x
 2.5.31: y = 7x
 2.5.32: y = 9x
 2.5.33: y = 1 2 x + 3
 2.5.34: y = 1 4 x  5
 2.5.35: y =  2 5 x  1
 2.5.36: y =  3 7 x  2
 2.5.37: 4x + y = 7
 2.5.38: 8x + y = 11
 2.5.39: 2x + 4y = 8
 2.5.40: 3x + 2y = 6
 2.5.41: 2x  3y = 5
 2.5.42: 3x  4y = 7
 2.5.43: x = 6
 2.5.44: y = 9
 2.5.45: y (4, 2) L L is parallel to y = 2x. 4 2 4 2 4 2 2 4
 2.5.46: y = 2x x y (3, 4) L L is parallel to y = 2x.
 2.5.47: y (2, 4) L L is perpendicular to y = 2x. 4 2 4 2 4 2 2 4
 2.5.48: y = 2x x y (1, 2) L L is perpendicular to y = 2x.
 2.5.49: Passing through (8, 10) and parallel to the line whose equation i...
 2.5.50: Passing through (2, 7) and parallel to the line whose equation is...
 2.5.51: Passing through (2, 3) and perpendicular to the line whose equatio...
 2.5.52: Passing through (4, 2) and perpendicular to the line whose equatio...
 2.5.53: Passing through (2, 2) and parallel to the line whose equation is ...
 2.5.54: Passing through (1, 3) and parallel to the line whose equation is ...
 2.5.55: Passing through (4, 7) and perpendicular to the line whose equatio...
 2.5.56: Passing through (5, 9) and perpendicular to the line whose equatio...
 2.5.57: The graph of f passes through (1, 5) and is perpendicular to the l...
 2.5.58: The graph of f passes through (2, 6) and is perpendicular to the l...
 2.5.59: The graph of f passes through (6, 4) and is perpendicular to the l...
 2.5.60: The graph of f passes through (5, 6) and is perpendicular to the l...
 2.5.61: The graph of f is perpendicular to the line whose equation is 3x  ...
 2.5.62: The graph of f is perpendicular to the line whose equation is 4x  ...
 2.5.63: The graph of f is the graph of g(x) = 4x  3 shifted down 2 units.
 2.5.64: The graph of f is the graph of g(x) = 2x  5 shifted up 3 units.
 2.5.65: What is the slope of a line that is parallel to the line whose equa...
 2.5.66: What is the slope of a line that is perpendicular to the line whose...
 2.5.67: In this exercise, you will use the blue line for the women shown on...
 2.5.68: In this exercise, you will use the red line for the men shown on th...
 2.5.69: The bar graph shows the number of smartphones sold in the United St...
 2.5.70: The bar graph shows the number of U.S. lawsuits by smartphone compa...
 2.5.71: a. Find the slope of the line segment representing Social Security....
 2.5.72: a. Find the slope of the line segment representing Social Security....
 2.5.73: Just as money doesnt buy happiness for individuals, the two dont ne...
 2.5.74: Describe how to write the equation of a line if its slope and a poi...
 2.5.75: Describe how to write the equation of a line if two points along th...
 2.5.76: If two lines are parallel, describe the relationship between their ...
 2.5.77: If two lines are perpendicular, describe the relationship between t...
 2.5.78: If you know a point on a line and you know the equation of a line p...
 2.5.79: In Example 3 on page 158, we developed a model that predicted Ameri...
 2.5.80: The lines whose equations are y = 1 3 x + 1 and y = 3x  2 are per...
 2.5.81: a. Use the statistical menu of your graphing utility to enter the s...
 2.5.82: Repeat Exercise 81 using the seven data points shown in the scatter...
 2.5.83: I can use any two points in a scatter plot to write the pointslope...
 2.5.84: I have linear functions that model changes for men and women over t...
 2.5.85: Some of the steel girders in this photo of the Eiffel Tower appear ...
 2.5.86: When writing equations of lines, its always easiest to begin by wri...
 2.5.87: The standard form of the equation of a line passing through (3, 1...
 2.5.88: If I change the subtraction signs to addition signs in y  12 = 8(x...
 2.5.89: y  5 = 2(x  1) is an equation of a line passing through (4, 11).
 2.5.90: The function {(1, 4), (3, 6), (5, 7), (11, 10)} can be described u...
 2.5.91: Determine the value of B so that the line whose equation is By = 8x...
 2.5.92: Determine the value of A so that the line whose equation is Ax + y ...
 2.5.93: Consider a line whose xintercept is 3 and whose yintercept is 6...
 2.5.94: Prove that the equation of a line passing through (a, 0) and (0, b)...
 2.5.95: If f(x) = 3x2  8x + 5, find f(2). (Section 2.1, Example 3)
 2.5.96: If f(x) = x2  3x + 4 and g(x) = 2x  5, find (fg)(1). (Section 2....
 2.5.97: The sum of the angles of a triangle is 180. Find the three angles o...
 2.5.98: a. Does (5, 6) satisfy 2x  y = 4? b. Does (5, 6) satisfy 3x ...
 2.5.99: Graph y = x  1 and 4x  3y = 24 in the same rectangular coordinat...
 2.5.100: Solve: 7x  2(2x + 4) = 3.
Solutions for Chapter 2.5: The Point SlopeForm of the Equation of a Line
Full solutions for Intermediate Algebra for College Students  6th Edition
ISBN: 9780321758934
Solutions for Chapter 2.5: The Point SlopeForm of the Equation of a Line
Get Full SolutionsThis textbook survival guide was created for the textbook: Intermediate Algebra for College Students, edition: 6. Chapter 2.5: The Point SlopeForm of the Equation of a Line includes 100 full stepbystep solutions. Intermediate Algebra for College Students was written by and is associated to the ISBN: 9780321758934. This expansive textbook survival guide covers the following chapters and their solutions. Since 100 problems in chapter 2.5: The Point SlopeForm of the Equation of a Line have been answered, more than 16040 students have viewed full stepbystep solutions from this chapter.

Back substitution.
Upper triangular systems are solved in reverse order Xn to Xl.

Block matrix.
A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

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).

Complete solution x = x p + Xn to Ax = b.
(Particular x p) + (x n in nullspace).

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib II· Condition numbers measure the sensitivity of the output to change in the input.

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

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!).

Identity matrix I (or In).
Diagonal entries = 1, offdiagonal entries = 0.

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.

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

Lucas numbers
Ln = 2,J, 3, 4, ... satisfy Ln = L n l +Ln 2 = A1 +A~, with AI, A2 = (1 ± /5)/2 from the Fibonacci matrix U~]' Compare Lo = 2 with Fo = O.

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

Particular solution x p.
Any solution to Ax = b; often x p has free variables = o.

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.

Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.
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