 2.1.1: The simplest mathematical model for relating two variables is the _...
 2.1.11: 2, 3
 2.1.12: 4, 1
 2.1.55: 1 3 2004
 2.1.2: For a line, the ratio of the change in to the change in is called t...
 2.1.3: Two lines are ________ if and only if their slopes are equal
 2.1.4: Two lines are ________ if and only if their slopes are negative rec...
 2.1.5: When the axis and axis have different units of measure, the slope...
 2.1.6: The prediction method ________ ________ is the method used to estim...
 2.1.7: Every line has an equation that can be written in ________ form.
 2.1.8: Match each equation of a line with its form. (a) (i) Vertical line ...
 2.1.9: (a) 10. (a) (b)
 2.1.10: a)
 2.1.13: 2468 2 4 6 8 y
 2.1.14: x 2468 2 4 6 8 y
 2.1.15: y 468 2 4 6 8
 2.1.16: x 246 2 4 6 y
 2.1.17: y 5x 3
 2.1.18: y x 10
 2.1.19: y x 6 1 2x 4 y
 2.1.20: y 3 2 y x 6 1
 2.1.21: 5x 2 0 3
 2.1.22: 3y 5 0
 2.1.23: 7x 6y 30
 2.1.24: 2x 3y 9
 2.1.25: y 3 0 y
 2.1.26: y 4 0
 2.1.27: x 5 0
 2.1.28: x 2 0
 2.1.29: 0, 9, 6, 0
 2.1.30: 12, 0, 0, 8
 2.1.31: 3, 2, 1, 6 2
 2.1.32: 2, 4, 4, 4
 2.1.33: 5, 7, 8, 7 2
 2.1.34: 2, 1, 4, 5 3
 2.1.35: 6, 1, 6, 4 0,
 2.1.36: 0, 10, 4, 0
 2.1.37: 11 2 , 4 3, 3 2, 1 3 6
 2.1.38: 7 8, 3 4, 5 4,1 4 1
 2.1.39: 4.8, 3.1, 5.2, 1.6
 2.1.40: 1.75, 8.3, 2.25, 2.6 4
 2.1.41: 1.75, 8.3, 2.25, 2.6 4
 2.1.42:
 2.1.43: 5,
 2.1.44:
 2.1.45: 8, 1, m
 2.1.46: 1, 5, m
 2.1.47: 5, 4, m 2
 2.1.48: 0, 9, m 2
 2.1.49: m 1, 6, 1 2 7, 2
 2.1.50: 1 2 m 1,
 2.1.51: 0, 2, m 3 0
 2.1.52: 0, 10, m 1
 2.1.53: 3, 6, m 2 0
 2.1.54: 0, 0, m 4
 2.1.56: 1 4 m 8,
 2.1.57: m 2, 5, 1 2 2, 3
 2.1.58: 3 4 m 2,
 2.1.59: 6, 1, m
 2.1.60: 10, 4, m
 2.1.61: 4, m 0
 2.1.62: m 0 1 2, 3 2 4, m 0 ,
 2.1.63: 5.1, 1.8, m 5
 2.1.64: 2.3, 8.5, m 2.5
 2.1.65: 2.3, 8.5, m 2.5
 2.1.66: 4, 3, 4, 4
 2.1.67: 4, 3, 4, 4
 2.1.68: 1, 4, 6, 4
 2.1.69: 2, 1 2, 1 2, 5
 2.1.70: 1, 1, 6, 2 3 2, 1
 2.1.71: 1 10, 3 5, 9 10, 9 5 1
 2.1.72: 4, 3 2, 4 3, 7 4
 2.1.73: 1, 0.6, 2, 0.6 8
 2.1.74: 8, 0.6, 2, 2.4
 2.1.75: 2, 1, , 2, 6, 2 1 3, 1 1,
 2.1.76: 1 5 2, 1, , 2, 6, 2 1 3
 2.1.77: 7 3, 8, 7 3, 1
 2.1.78: 1.5, 2, 1.5, 0.2 7
 2.1.79: 3 L1 L1
 2.1.80: L2 L2: y : y 4x 7 1 3 x 3 L1
 2.1.81: L1: y x 5 1 2 x 3 L
 2.1.82: 1: y 4 5 L1: y x 5 1
 2.1.83: 4, 1 L1 L
 2.1.84: 1, 3, 5, 5 2: 0, 3, 4, 1 L1
 2.1.85: L : 4, 8, 4, 2 1: 3, 6
 2.1.86: L2: 3, 5, 1, 1 3 L 2: 0, 1, 5, 7 3 L1 L
 2.1.87: 4x 2y 3, 2, 1 x
 2.1.88: x y 7, 3, 2
 2.1.89: 3x 4y 7,
 2.1.90: 5x 3y 0,
 2.1.91: y 3 0,
 2.1.92: y 2 0,
 2.1.93: x 4 0, 3, 2 x
 2.1.94: x 2 0, 5, 1
 2.1.95: x y 4, 2.5, 6.8
 2.1.96: 6x 2y 9, 3.9, 1.4 x
 2.1.97: y 0, 3 y 0, 4 x
 2.1.98: x
 2.1.99: x
 2.1.100: x
 2.1.101: Point on line: intercept: intercept
 2.1.102: Point on line: intercept: intercept:
 2.1.103: (a)
 2.1.104: (a)
 2.1.105: (a)
 2.1.106: (a)
 2.1.107: 4, 1, 2, 3 6
 2.1.108: 6, 5, 1, 8
 2.1.109: 3, 5 2, 7, 1
 2.1.110: 1 2, 4, 7 2, 5 4
 2.1.111: SALES The following are the slopes of lines representing annual sal...
 2.1.112: REVENUE The following are the slopes of lines representing daily re...
 2.1.113: AVERAGE SALARY The graph shows the average salaries for senior high...
 2.1.114: SALES The graph shows the sales (in billions of dollars) for Apple ...
 2.1.115: ROAD GRADE You are driving on a road that has a 6% uphill grade (se...
 2.1.116: ROAD GRADE From the top of a mountain road, a surveyor takes severa...
 2.1.117: $2540 $125 decrease per year
 2.1.118: $156 $4.50 increase per year
 2.1.119: DEPRECIATION The value of a molding machine years after it is purch...
 2.1.120: COST The cost of producing computer laptop bags is given by Explain...
 2.1.121: DEPRECIATION A sub shop purchases a used pizza oven for $875. After...
 2.1.122: DEPRECIATION A school district purchases a highvolume printer, cop...
 2.1.123: SALES A discount outlet is offering a 20% discount on all items. Wr...
 2.1.124: HOURLY WAGE A microchip manufacturer pays its assembly line workers...
 2.1.125: MONTHLY SALARY A pharmaceutical salesperson receives a monthly sala...
 2.1.126: BUSINESS COSTS A sales representative of a company using a personal...
 2.1.127: CASH FLOW PER SHARE The cash flow per share for the Timberland Co. ...
 2.1.128: NUMBER OF STORES In 2003 there were 1078 J.C. Penney stores and in ...
 2.1.129: COLLEGE ENROLLMENT The Pennsylvania State University had enrollment...
 2.1.130: COLLEGE ENROLLMENT The University of Florida had enrollments of 46,...
 2.1.131: COST, REVENUE, AND PROFIT A roofing contractor purchases a shingle ...
 2.1.132: RENTAL DEMAND A real estate office handles an apartment complex wit...
 2.1.133: GEOMETRY The length and width of a rectangular garden are 15 meters...
 2.1.134: AVERAGE ANNUAL SALARY The average salaries (in millions of dollars)...
 2.1.135: DATA ANALYSIS: NUMBER OF DOCTORS The numbers of doctors of osteopat...
 2.1.136: DATA ANALYSIS: AVERAGE SCORES An instructor gives regular 20point ...
 2.1.137: A line with a slope of is steeper than a line with a slope of
 2.1.138: The line through and and the line through and are parallel.
 2.1.139: Explain how you could show that the points and are the vertices of ...
 2.1.140: Explain why the slope of a vertical line is said to be undefined.
 2.1.141: With the information shown in the graphs, is it possible to determi...
 2.1.142: The slopes of two lines are and Which is steeper? Explain
 2.1.143: Use a graphing utility to compare the slopes of the lines where 1, ...
 2.1.144: Find and in terms of and respectively (see figure). Then use the Py...
 2.1.145: THINK ABOUT IT Is it possible for two lines with positive slopes to...
 2.1.146: CAPSTONE Match the description of the situation with its graph. Als...
Solutions for Chapter 2.1: Linear Equations in Two Variables
Full solutions for Algebra and Trigonometry  8th Edition
ISBN: 9781439048474
Solutions for Chapter 2.1: Linear Equations in Two Variables
Get Full SolutionsChapter 2.1: Linear Equations in Two Variables includes 146 full stepbystep solutions. Algebra and Trigonometry was written by and is associated to the ISBN: 9781439048474. This textbook survival guide was created for the textbook: Algebra and Trigonometry, edition: 8. This expansive textbook survival guide covers the following chapters and their solutions. Since 146 problems in chapter 2.1: Linear Equations in Two Variables have been answered, more than 52007 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).

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.

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.

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

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.

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

Orthogonal subspaces.
Every v in V is orthogonal to every w in W.

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).

Positive definite matrix A.
Symmetric matrix with positive eigenvalues and positive pivots. Definition: x T Ax > 0 unless x = O. Then A = LDLT with diag(D» O.

Random matrix rand(n) or randn(n).
MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

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).

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

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

Skewsymmetric matrix K.
The transpose is K, since Kij = Kji. Eigenvalues are pure imaginary, eigenvectors are orthogonal, eKt is an orthogonal matrix.

Solvable system Ax = b.
The right side b is in the column space of A.

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

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·

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

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