 1.4.1: The slope of a vertical line is _____________ ; the slope of a hori...
 1.4.2: For the line 2x + 3y = 6, the xintercept is ________ and the yint...
 1.4.3: A horizontal line is given by an equation of the form _________, wh...
 1.4.4: Vertical lines have an undefined slope.
 1.4.5: The slope of the line 2y = 3x + 5 is 3.
 1.4.6: he point (1, 2) is on the line 2x + y = 4.
 1.4.7: Two nonvertical lines have slopes m1 and m2, respectively. The line...
 1.4.8: The lines y = 2x + 3 and y = ax + 5 are parallel if a = ________.
 1.4.9: The lines y = 2x  1 and y = ax + 2 are perpendicular if a = ________.
 1.4.10: Perpendicular lines have slopes that are reciprocals of one another.
 1.4.11: In 1114, (a) find the slope of the line and (b) interpret the slope.
 1.4.12: In 1114, (a) find the slope of the line and (b) interpret the slope.
 1.4.13: In 1114, (a) find the slope of the line and (b) interpret the slope.
 1.4.14: In 1114, (a) find the slope of the line and (b) interpret the slope.
 1.4.15: In 1522, plot each pair of points and determine the slope of the li...
 1.4.16: In 1522, plot each pair of points and determine the slope of the li...
 1.4.17: In 1522, plot each pair of points and determine the slope of the li...
 1.4.18: In 1522, plot each pair of points and determine the slope of the li...
 1.4.19: In 1522, plot each pair of points and determine the slope of the li...
 1.4.20: In 1522, plot each pair of points and determine the slope of the li...
 1.4.21: In 1522, plot each pair of points and determine the slope of the li...
 1.4.22: In 1522, plot each pair of points and determine the slope of the li...
 1.4.23: In 2330, graph the line containing the point P and having slope m
 1.4.24: In 2330, graph the line containing the point P and having slope m
 1.4.25: In 2330, graph the line containing the point P and having slope m
 1.4.26: In 2330, graph the line containing the point P and having slope m
 1.4.27: In 2330, graph the line containing the point P and having slope m
 1.4.28: In 2330, graph the line containing the point P and having slope m
 1.4.29: In 2330, graph the line containing the point P and having slope m
 1.4.30: In 2330, graph the line containing the point P and having slope m
 1.4.31: In 3136, the slope and a point on a line are given. Use this inform...
 1.4.32: In 3136, the slope and a point on a line are given. Use this inform...
 1.4.33: In 3136, the slope and a point on a line are given. Use this inform...
 1.4.34: In 3136, the slope and a point on a line are given. Use this inform...
 1.4.35: In 3136, the slope and a point on a line are given. Use this inform...
 1.4.36: In 3136, the slope and a point on a line are given. Use this inform...
 1.4.37: In 3744, find an equation of the line L
 1.4.38: In 3744, find an equation of the line L
 1.4.39: In 3744, find an equation of the line L
 1.4.40: In 3744, find an equation of the line L
 1.4.41: In 3744, find an equation of the line L
 1.4.42: In 3744, find an equation of the line L
 1.4.43: In 3744, find an equation of the line L
 1.4.44: In 3744, find an equation of the line L
 1.4.45: In 4570, find an equation for the line with the given properties. E...
 1.4.46: In 4570, find an equation for the line with the given properties. E...
 1.4.47: In 4570, find an equation for the line with the given properties. E...
 1.4.48: In 4570, find an equation for the line with the given properties. E...
 1.4.49: In 4570, find an equation for the line with the given properties. E...
 1.4.50: In 4570, find an equation for the line with the given properties. E...
 1.4.51: In 4570, find an equation for the line with the given properties. E...
 1.4.52: In 4570, find an equation for the line with the given properties. E...
 1.4.53: In 4570, find an equation for the line with the given properties. E...
 1.4.54: In 4570, find an equation for the line with the given properties. E...
 1.4.55: In 4570, find an equation for the line with the given properties. E...
 1.4.56: In 4570, find an equation for the line with the given properties. E...
 1.4.57: In 4570, find an equation for the line with the given properties. E...
 1.4.58: In 4570, find an equation for the line with the given properties. E...
 1.4.59: In 4570, find an equation for the line with the given properties. E...
 1.4.60: In 4570, find an equation for the line with the given properties. E...
 1.4.61: In 4570, find an equation for the line with the given properties. E...
 1.4.62: In 4570, find an equation for the line with the given properties. E...
 1.4.63: In 4570, find an equation for the line with the given properties. E...
 1.4.64: In 4570, find an equation for the line with the given properties. E...
 1.4.65: In 4570, find an equation for the line with the given properties. E...
 1.4.66: In 4570, find an equation for the line with the given properties. E...
 1.4.67: In 4570, find an equation for the line with the given properties. E...
 1.4.68: In 4570, find an equation for the line with the given properties. E...
 1.4.69: In 4570, find an equation for the line with the given properties. E...
 1.4.70: In 4570, find an equation for the line with the given properties. E...
 1.4.71: In 7190, find the slope and yintercept of each line. Graph the lin...
 1.4.72: In 7190, find the slope and yintercept of each line. Graph the lin...
 1.4.73: In 7190, find the slope and yintercept of each line. Graph the lin...
 1.4.74: In 7190, find the slope and yintercept of each line. Graph the lin...
 1.4.75: In 7190, find the slope and yintercept of each line. Graph the lin...
 1.4.76: In 7190, find the slope and yintercept of each line. Graph the lin...
 1.4.77: In 7190, find the slope and yintercept of each line. Graph the lin...
 1.4.78: In 7190, find the slope and yintercept of each line. Graph the lin...
 1.4.79: In 7190, find the slope and yintercept of each line. Graph the lin...
 1.4.80: In 7190, find the slope and yintercept of each line. Graph the lin...
 1.4.81: In 7190, find the slope and yintercept of each line. Graph the lin...
 1.4.82: In 7190, find the slope and yintercept of each line. Graph the lin...
 1.4.83: In 7190, find the slope and yintercept of each line. Graph the lin...
 1.4.84: In 7190, find the slope and yintercept of each line. Graph the lin...
 1.4.85: In 7190, find the slope and yintercept of each line. Graph the lin...
 1.4.86: In 7190, find the slope and yintercept of each line. Graph the lin...
 1.4.87: In 7190, find the slope and yintercept of each line. Graph the lin...
 1.4.88: In 7190, find the slope and yintercept of each line. Graph the lin...
 1.4.89: In 7190, find the slope and yintercept of each line. Graph the lin...
 1.4.90: In 7190, find the slope and yintercept of each line. Graph the lin...
 1.4.91: In 91100, (a) find the intercepts of the graph of each equation and...
 1.4.92: In 91100, (a) find the intercepts of the graph of each equation and...
 1.4.93: In 91100, (a) find the intercepts of the graph of each equation and...
 1.4.94: In 91100, (a) find the intercepts of the graph of each equation and...
 1.4.95: In 91100, (a) find the intercepts of the graph of each equation and...
 1.4.96: In 91100, (a) find the intercepts of the graph of each equation and...
 1.4.97: In 91100, (a) find the intercepts of the graph of each equation and...
 1.4.98: In 91100, (a) find the intercepts of the graph of each equation and...
 1.4.99: In 91100, (a) find the intercepts of the graph of each equation and...
 1.4.100: In 91100, (a) find the intercepts of the graph of each equation and...
 1.4.101: Find an equation of the xaxis.
 1.4.102: Find an equation of the yaxis.
 1.4.103: In 103106, the equations of two lines are given. Determine if the l...
 1.4.104: In 103106, the equations of two lines are given. Determine if the l...
 1.4.105: In 103106, the equations of two lines are given. Determine if the l...
 1.4.106: In 103106, the equations of two lines are given. Determine if the l...
 1.4.107: In 107110, write an equation of each line. Express your answer usin...
 1.4.108: In 107110, write an equation of each line. Express your answer usin...
 1.4.109: In 107110, write an equation of each line. Express your answer usin...
 1.4.110: In 107110, write an equation of each line. Express your answer usin...
 1.4.111: Use slopes to show that the triangle whose vertices are (2, 5), (1...
 1.4.112: Use slopes to show that the quadrilateral whose vertices are (1, 1...
 1.4.113: Use slopes to show that the quadrilateral whose vertices are (1, 0...
 1.4.114: Use slopes and the distance formula to show that the quadrilateral ...
 1.4.115: A truck rental company rents a moving truck for one day by charging...
 1.4.116: The fixed costs of operating a business are the costs incurred rega...
 1.4.117: The annual fixed costs for owning a small sedan are $1289, assuming...
 1.4.118: Dan receives $375 per week for selling new and used cars at a car d...
 1.4.119: Dan receives $375 per week for selling new and used cars at a car d...
 1.4.120: Florida Power & Light Company supplies electricity to residential c...
 1.4.121: The relationship between Celsius (C) and Fahrenheit (F) degrees of ...
 1.4.122: The Kelvin (K) scale for measuring temperature is obtained by addin...
 1.4.123: The Kelvin (K) scale for measuring temperature is obtained by addin...
 1.4.124: A report in the Child Trends DataBase indicated that, in 2000, 20.6...
 1.4.125: A cereal company finds that the number of people who will buy one o...
 1.4.126: Show that the line containing the points (a, b) and (b, a), a b, is...
 1.4.127: The equation 2x  y = C defines a family of lines, one line for eac...
 1.4.128: Prove that if two nonvertical lines have slopes whose product is 1...
 1.4.129: Which of the following equations might have the graph shown? (More ...
 1.4.130: Which of the following equations might have the graph shown? (More ...
 1.4.131: The figure shows the graph of two parallel lines. Which of the foll...
 1.4.132: The figure shows the graph of two perpendicular lines. Which of the...
 1.4.133: The accepted symbol used to denote the slope of a line is the lette...
 1.4.134: The term grade is used to describe the inclination of a road. How d...
 1.4.135: Carpenters use the term pitch to describe the steepness of staircas...
 1.4.136: Can the equation of every line be written in slope intercept form? ...
 1.4.137: Does every line have exactly one xintercept and one yintercept? A...
 1.4.138: What can you say about two lines that have equal slopes and equal y...
 1.4.139: What can you say about two lines with the same xintercept and the ...
 1.4.140: If two distinct lines have the same slope, but different xintercep...
 1.4.141: If two distinct lines have the same yintercept, but different slop...
 1.4.142: Which form of the equation of a line do you prefer to use? Justify ...
 1.4.143: A student is asked to find the slope of the line joining (3, 2) an...
 1.4.144: Open the slope applet. Move point B around the Cartesian plane with...
Solutions for Chapter 1.4: Lines
Full solutions for Precalculus Enhanced with Graphing Utilities  6th Edition
ISBN: 9780132854351
Solutions for Chapter 1.4: Lines
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Precalculus Enhanced with Graphing Utilities was written by and is associated to the ISBN: 9780132854351. Chapter 1.4: Lines includes 144 full stepbystep solutions. Since 144 problems in chapter 1.4: Lines have been answered, more than 53152 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Precalculus Enhanced with Graphing Utilities, edition: 6.

CayleyHamilton Theorem.
peA) = det(A  AI) has peA) = zero matrix.

Characteristic equation det(A  AI) = O.
The n roots are the eigenvalues of A.

Column space C (A) =
space of all combinations of the columns of A.

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

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).

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.

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

Orthogonal matrix Q.
Square matrix with orthonormal columns, so QT = Ql. Preserves length and angles, IIQxll = IIxll and (QX)T(Qy) = xTy. AlllAI = 1, with orthogonal eigenvectors. Examples: Rotation, reflection, permutation.

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

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).

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.

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

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.