 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 52748 students have viewed full stepbystep solutions from this chapter.

Adjacency matrix of a graph.
Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

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).

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

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

Full column rank r = n.
Independent columns, N(A) = {O}, no free variables.

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

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.

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

lAII = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n  1, volume of box = I det( A) I.

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

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.

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.

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

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.

Singular Value Decomposition
(SVD) A = U:E VT = (orthogonal) ( diag)( orthogonal) First r columns of U and V are orthonormal bases of C (A) and C (AT), AVi = O'iUi with singular value O'i > O. Last columns are orthonormal bases of nullspaces.

Spanning set.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!

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