 2.4.1: Data presented in a visual form as a set of points is called a/an _...
 2.4.2: The equation Ax + By = C, where A and B are not both zero, is calle...
 2.4.3: The xcoordinate of a point where a graph crosses the xaxis is cal...
 2.4.4: The ycoordinate of a point where a graph crosses the yaxis is cal...
 2.4.5: The slope, m, of a line through the distinct points (x1, y1) and (x...
 2.4.6: If a line rises from left to right, the line has ______________ slope.
 2.4.7: If a line falls from left to right, the line has ______________ slope.
 2.4.8: The slope of a horizontal line is ______________.
 2.4.9: The slope of a vertical line is ______________.
 2.4.10: The slopeintercept form of the equation of a line is _____________...
 2.4.11: In order to graph the line whose equation is y = 2 5 x + 3, begin b...
 2.4.12: The graph of the equation y = 3 is a/an ______________ line.
 2.4.13: The graph of the equation x = 2 is a/an ______________ line.
 2.4.14: The slope of the line through the distinct points (x1, y1) and (x2,...
 2.4.15: (2, 4) and (3, 8)
 2.4.16: (3, 1) and (5, 4)
 2.4.17: (1, 4) and (2, 5)
 2.4.18: (3, 2) and (2, 5)
 2.4.19: (2, 5) and (1, 5)
 2.4.20: (6, 3) and (4, 3)
 2.4.21: (7, 1) and (4, 3)
 2.4.22: (2, 1) and (6, 3)
 2.4.23: (7, 4) and (3, 6)
 2.4.24: (3, 4) and (1, 6)
 2.4.25: a 7 2 , 2b and a 7 2 , 1 4 b
 2.4.26: a 3 2 , 6b and a 3 2 , 1 6 b
 2.4.27: y L1 L2 L3 4 2 4 2 2 2
 2.4.28: L1 L2 L3 4 2 4 4 2 2 4
 2.4.29: y = 2x + 1
 2.4.30: y = 3x + 2
 2.4.31: y = 2x + 1
 2.4.32: y = 3x + 2
 2.4.33: f(x) = 3 4 x  2
 2.4.34: f(x) = 3 4 x  3
 2.4.35: f(x) =  3 5 x + 7
 2.4.36: f(x) =  2 5 x + 6
 2.4.37: y =  1 2 x
 2.4.38: y =  1 3 x
 2.4.39: y =  1 2
 2.4.40: y =  1 3
 2.4.41: 2x + y = 0
 2.4.42: 3x + y = 0
 2.4.43: 5y = 4x
 2.4.44: 4y = 3x
 2.4.45: 3x + y = 2
 2.4.46: 2x + y = 4
 2.4.47: 5x + 3y = 15
 2.4.48: 7x + 2y = 14
 2.4.49: y = 3
 2.4.50: y = 5
 2.4.51: f(x) = 2
 2.4.52: f(x) = 4
 2.4.53: 3y = 18
 2.4.54: 5y = 30
 2.4.55: f(x) = 2
 2.4.56: f(x) = 1
 2.4.57: x = 5
 2.4.58: x = 4
 2.4.59: 3x = 12
 2.4.60: 4x = 12
 2.4.61: x = 0
 2.4.62: y = 0
 2.4.63: (0, a) and (b, 0)
 2.4.64: (a, 0) and (0, b)
 2.4.65: (a, b) and (a, b + c)
 2.4.66: (a  b, c) and (a, a + c)
 2.4.67: Ax + By = C
 2.4.68: Ax = By  C
 2.4.69: (3, y) and (1, 4), m = 3
 2.4.70: (2, y) and (4, 4), m = 1 3
 2.4.71: 3x  4f(x) = 6
 2.4.72: 6x  5f(x) = 20
 2.4.73: If one point on a line is (3, 1) and the lines slope is 2, find t...
 2.4.74: If one point on a line is (2, 6) and the lines slope is  3 2 , fi...
 2.4.75: List the slopes m1 , m2 , m3 , and m4 in order of decreasing size.
 2.4.76: List the yintercepts b1 , b2 , b3 , and b4 in order of decreasing ...
 2.4.77: The linear function f(x) = 55.7x + 60.1 models the number of smartp...
 2.4.78: The linear function f(x) = 2x + 10 models the amount, f(x), in bill...
 2.4.79: The linear function f(x) = 0.52x + 24.7 models the percentage of U...
 2.4.80: The linear function f(x) = 0.28x + 1.7 models the percentage of U....
 2.4.81: a. What percentage of marriages in which the wife is under 18 when ...
 2.4.82: a. What percentage of marriages in which the wife is over age 25 wh...
 2.4.83: Shown, again, is the scatter plot that indicates a relationship bet...
 2.4.84: On Super Bowl Sunday, viewers of the big game expect to be entertai...
 2.4.85: In 1968, 18% of the grades for students entering college were A (A,...
 2.4.86: In 1968, 23% of the grades for students entering college were C (C,...
 2.4.87: What is a scatter plot?
 2.4.88: What is a regression line?
 2.4.89: What is the standard form of the equation of a line?
 2.4.90: What is an xintercept of a graph?
 2.4.91: What is a yintercept of a graph?
 2.4.92: If you are given the standard form of the equation of a line, expla...
 2.4.93: If you are given the standard form of the equation of a line, expla...
 2.4.94: What is the slope of a line?
 2.4.95: Describe how to calculate the slope of a line passing through two p...
 2.4.96: What does it mean if the slope of a line is zero?
 2.4.97: What does it mean if the slope of a line is undefined?
 2.4.98: Describe how to find the slope of a line whose equation is given.
 2.4.99: Describe how to graph a line using the slope and yintercept. Provi...
 2.4.100: Describe the graph of y = b.
 2.4.101: Describe the graph of x = a.
 2.4.102: If the graph of a function is not a straight line, explain how to f...
 2.4.103: Take another look at the scatter plot in Exercise 83. Although ther...
 2.4.104: Use a graphing utility to verify any three of your handdrawn graphs...
 2.4.105: y = 2x + 4
 2.4.106: y = 3x + 6
 2.4.107: f(x) =  1 2 x  5
 2.4.108: f(x) = 3 4 x  2
 2.4.109: The graph of my linear function at first rose from left to right, r...
 2.4.110: A linear function that models tuition and fees at public fouryear ...
 2.4.111: The function S(x) = 49,100x + 1700 models the average salary for a ...
 2.4.112: The federal minimum wage was $5.15 per hour from 1997 through 2006,...
 2.4.113: A linear function with nonnegative slope has a graph that rises fro...
 2.4.114: Every line in the rectangular coordinate system has an equation tha...
 2.4.115: The graph of the linear function 5x + 6y = 30 is a line passing thr...
 2.4.116: The graph of x = 7 in the rectangular coordinate system is the sing...
 2.4.117: x + y = 12; xintercept = 2; yintercept = 4
 2.4.118: x + y = 12; yintercept = 6; slope = 1 2
 2.4.119: For the linear function f(x) = mx + b, a. Find f(x1 + x2). b. Find ...
 2.4.120: Simplify: 4x2 y3 2 . (Section 1.6, Example 9)
 2.4.121: Multiply and write the answer in scientific notation: (8 * 107 )(4...
 2.4.122: Simplify: 5  [3(x  4)  6x]. (Section 1.2, Example 14)
 2.4.123: Write the equation y  5 = 7(x + 4) in slopeintercept form.
 2.4.124: Write the equation y + 3 =  7 3 (x  1) in slopeintercept form.
 2.4.125: The equation of a line is x + 4y  8 = 0. a. Write the equation in ...
Solutions for Chapter 2.4: Linear Functions and Slope
Full solutions for Intermediate Algebra for College Students  6th Edition
ISBN: 9780321758934
Solutions for Chapter 2.4: Linear Functions and Slope
Get Full SolutionsIntermediate 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. This textbook survival guide was created for the textbook: Intermediate Algebra for College Students, edition: 6. Chapter 2.4: Linear Functions and Slope includes 125 full stepbystep solutions. Since 125 problems in chapter 2.4: Linear Functions and Slope have been answered, more than 9802 students have viewed full stepbystep solutions from this chapter.

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

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

Determinant IAI = det(A).
Defined by det I = 1, sign reversal for row exchange, and linearity in each row. Then IAI = 0 when A is singular. Also IABI = IAIIBI and

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

Fast Fourier Transform (FFT).
A factorization of the Fourier matrix Fn into e = log2 n matrices Si times a permutation. Each Si needs only nl2 multiplications, so Fnx and Fn1c can be computed with ne/2 multiplications. Revolutionary.

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

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

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.

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

Nilpotent matrix N.
Some power of N is the zero matrix, N k = o. The only eigenvalue is A = 0 (repeated n times). Examples: triangular matrices with zero diagonal.

Outer product uv T
= column times row = rank one matrix.

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

Pseudoinverse A+ (MoorePenrose inverse).
The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

Reflection matrix (Householder) Q = I 2uuT.
Unit vector u is reflected to Qu = u. All x intheplanemirroruTx = o have Qx = x. Notice QT = Q1 = Q.

Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

Semidefinite matrix A.
(Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.

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