 43.1: Write an equation in slopeintercept form of the line with the give...
 43.2: Write an equation in slopeintercept form of the line with the give...
 43.3: Write an equation in slopeintercept form of the line shown in each...
 43.4: Write an equation in slopeintercept form of the line shown in each...
 43.5: Graph each equation.
 43.6: Graph each equation.
 43.7: Graph each equation.
 43.8: Graph each equation.
 43.9: MONEY For Exercises 911, use the following information. Suppose you...
 43.10: MONEY For Exercises 911, use the following information. Suppose you...
 43.11: MONEY For Exercises 911, use the following information. Suppose you...
 43.12: Write an equation in slopeintercept form of the line with the give...
 43.13: Write an equation in slopeintercept form of the line with the give...
 43.14: Write an equation in slopeintercept form of the line with the give...
 43.15: Write an equation in slopeintercept form of the line with the give...
 43.16: Write an equation in slopeintercept form of the line with the give...
 43.17: Write an equation in slopeintercept form of the line with the give...
 43.18: Write an equation in slopeintercept form of the line shown in each...
 43.19: Write an equation in slopeintercept form of the line shown in each...
 43.20: Write an equation in slopeintercept form of the line shown in each...
 43.21: Write an equation in slopeintercept form of the line shown in each...
 43.22: Write an equation in slopeintercept form of the line shown in each...
 43.23: Write an equation in slopeintercept form of the line shown in each...
 43.24: Graph each equation.
 43.25: Graph each equation.
 43.26: Graph each equation.
 43.27: Graph each equation.
 43.28: Graph each equation.
 43.29: Graph each equation.
 43.30: Graph each equation.
 43.31: Graph each equation.
 43.32: Graph each equation.
 43.33: BICYCLES For Exercises 33 and 34, use the following information. A ...
 43.34: BICYCLES For Exercises 33 and 34, use the following information. A ...
 43.35: ANALYZE GRAPHS For Exercises 35 and 36, Book Sales 1 2 3 4 Years Si...
 43.36: ANALYZE GRAPHS For Exercises 35 and 36, Book Sales 1 2 3 4 Years Si...
 43.37: COLLEGE For Exercises 37 and 38, use the following information For ...
 43.38: COLLEGE For Exercises 37 and 38, use the following information For ...
 43.39: Write an equation of the line with the given slope and yintercept.
 43.40: Write an equation of the line with the given slope and yintercept.
 43.41: Write an equation of the line with the given slope and yintercept.
 43.42: Write an equation of the line with the given slope and yintercept.
 43.43: Write an equation of a horizontal line that crosses the yaxis at (...
 43.44: Write an equation of a line that passes through the origin with slo...
 43.45: CHALLENGE Summarize the characteristic that the graphs of y = 2x + ...
 43.46: OPEN ENDED Draw a graph representing a realworld linear function a...
 43.47: Writing in Math Use the data about online shipping costs on page 20...
 43.48: Which statement O 12345 100 105 110 115 y x is most strongly suppor...
 43.49: REVIEW Sam is going to put a border around a poster he is making fo...
 43.50: Suppose y varies directly as x. Write a direct variation equation t...
 43.51: Suppose y varies directly as x. Write a direct variation equation t...
 43.52: Find the rate of change represented in each table or graph.
 43.53: Find the rate of change represented in each table or graph.
 43.54: Find the rate of change represented in each table or graph.
 43.55: LIFE SCIENCE A Laysan albatross tracked by biologists flew more tha...
 43.56: PREREQUISITE SKILL Find the slope of the line that passes through e...
 43.57: PREREQUISITE SKILL Find the slope of the line that passes through e...
 43.58: PREREQUISITE SKILL Find the slope of the line that passes through e...
Solutions for Chapter 43: Investigating SlopeIntercept Form
Full solutions for Algebra 1, Student Edition (MERRILL ALGEBRA 1)  1st Edition
ISBN: 9780078738227
Solutions for Chapter 43: Investigating SlopeIntercept Form
Get Full SolutionsAlgebra 1, Student Edition (MERRILL ALGEBRA 1) was written by and is associated to the ISBN: 9780078738227. Since 58 problems in chapter 43: Investigating SlopeIntercept Form have been answered, more than 34493 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Algebra 1, Student Edition (MERRILL ALGEBRA 1) , edition: 1. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 43: Investigating SlopeIntercept Form includes 58 full stepbystep solutions.

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!

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.

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).

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

Cross product u xv in R3:
Vector perpendicular to u and v, length Ilullllvlll sin el = area of parallelogram, u x v = "determinant" of [i j k; UI U2 U3; VI V2 V3].

Cyclic shift
S. Permutation with S21 = 1, S32 = 1, ... , finally SIn = 1. Its eigenvalues are the nth roots e2lrik/n of 1; eigenvectors are columns of the Fourier matrix F.

Dimension of vector space
dim(V) = number of vectors in any basis for V.

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.

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.

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

Incidence matrix of a directed graph.
The m by n edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and j .

Inverse matrix AI.
Square matrix with AI A = I and AAl = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B1 AI and (AI)T. Cofactor formula (Al)ij = Cji! detA.

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

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

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

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.

Rank r (A)
= number of pivots = dimension of column space = dimension of row space.

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

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