 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 29505 students have viewed full stepbystep solutions from this chapter.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

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

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

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

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.

Hessenberg matrix H.
Triangular matrix with one extra nonzero adjacent diagonal.

Hilbert matrix hilb(n).
Entries HU = 1/(i + j 1) = Jd X i 1 xj1dx. Positive definite but extremely small Amin and large condition number: H is illconditioned.

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

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

Nullspace matrix N.
The columns of N are the n  r special solutions to As = O.

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

Permutation matrix P.
There are n! orders of 1, ... , n. The n! P 's have the rows of I in those orders. P A puts the rows of A in the same order. P is even or odd (det P = 1 or 1) based on the number of row exchanges to reach I.

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

Rayleigh quotient q (x) = X T Ax I x T x for symmetric A: Amin < q (x) < Amax.
Those extremes are reached at the eigenvectors x for Amin(A) and Amax(A).

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

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

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).