 45.1: Write the pointslope form of an equation for the line that passes ...
 45.2: Write the pointslope form of an equation for the line that passes ...
 45.3: Write the pointslope form of an equation for the line that passes ...
 45.4: Write each equation in standard form.
 45.5: Write each equation in standard form.
 45.6: Write each equation in standard form.
 45.7: Write each equation in slopeintercept form.
 45.8: Write each equation in slopeintercept form.
 45.9: Write each equation in slopeintercept form.
 45.10: GEOMETRY For Exercises 10 and 11, use y O x (1, 3) (4, 1) (6, 3) (3...
 45.11: GEOMETRY For Exercises 10 and 11, use y O x (1, 3) (4, 1) (6, 3) (3...
 45.12: Write the pointslope form of an equation for the line that passes ...
 45.13: Write the pointslope form of an equation for the line that passes ...
 45.14: Write the pointslope form of an equation for the line that passes ...
 45.15: Write the pointslope form of an equation for the line that passes ...
 45.16: Write the pointslope form of an equation for the line that passes ...
 45.17: Write the pointslope form of an equation for the line that passes ...
 45.18: Write the pointslope form of an equation for the horizontal line t...
 45.19: A horizontal line passes through (0, 7). Write the pointslope form...
 45.20: Write each equation in standard form.
 45.21: Write each equation in standard form.
 45.22: Write each equation in standard form.
 45.23: Write each equation in standard form.
 45.24: Write each equation in standard form.
 45.25: Write each equation in standard form.
 45.26: Write each equation in standard form.
 45.27: Write each equation in standard form.
 45.28: Write each equation in slopeintercept form.
 45.29: Write each equation in slopeintercept form.
 45.30: Write each equation in slopeintercept form.
 45.31: Write each equation in slopeintercept form.
 45.32: Write each equation in slopeintercept form.
 45.33: Write each equation in slopeintercept form.
 45.34: Write each equation in slopeintercept form.
 45.35: Write each equation in slopeintercept form.
 45.36: BUSINESS For Exercises 3638, use the following information. A home ...
 45.37: BUSINESS For Exercises 3638, use the following information. A home ...
 45.38: BUSINESS For Exercises 3638, use the following information. A home ...
 45.39: MOVIES For Exercises 3941, use the U.S. Movie Screens 20 0 Number (...
 45.40: MOVIES For Exercises 3941, use the U.S. Movie Screens 20 0 Number (...
 45.41: MOVIES For Exercises 3941, use the U.S. Movie Screens 20 0 Number (...
 45.42: Write each equation in standard form.
 45.43: Write each equation in standard form.
 45.44: Write each equation in standard form.
 45.45: Write each equation in slopeintercept form.
 45.46: Write each equation in slopeintercept form.
 45.47: Write each equation in slopeintercept form.
 45.48: Write the pointslope form, slopeintercept form, and standard form...
 45.49: Line passes through (1, 6) with slope _3 2 . Write the pointslope...
 45.50: FIND THE ERROR Tanya and Akira wrote the pointslope form of an equ...
 45.51: OPEN ENDED Compose a reallife scenario that has a constant rate of...
 45.52: REASONING Find an equation for the line that passes through (4, 8)...
 45.53: REASONING Barometric pressure is a linear function of altitude. At ...
 45.54: CHALLENGE A line contains the points (9, 1) and (5, 5). Make a conv...
 45.55: Writing in Math Demonstrate how you can use the slope formula to wr...
 45.56: What is the equation of the line that passes through (0, 1), and th...
 45.57: REVIEW What is the slope of the equation of the line that passes th...
 45.58: Write the slopeintercept form of an equation of the line that sati...
 45.59: Write the slopeintercept form of an equation of the line that sati...
 45.60: Write the slopeintercept form of an equation of the line that sati...
 45.61: Write the slopeintercept form of an equation of the line that sati...
 45.62: WATER The table shows the number of gallons Number of Minutes 1234 ...
 45.63: Solve each equation.
 45.64: Solve each equation.
 45.65: Solve each equation.
 45.66: Evaluate (25  4) ( 2 2  1 3 ).
 45.67: PREREQUISITE SKILL Write the slopeintercept form of an equation fo...
 45.68: PREREQUISITE SKILL Write the slopeintercept form of an equation fo...
 45.69: PREREQUISITE SKILL Write the slopeintercept form of an equation fo...
Solutions for Chapter 45: Writing Equations in PointSlope Form
Full solutions for Algebra 1, Student Edition (MERRILL ALGEBRA 1)  1st Edition
ISBN: 9780078738227
Solutions for Chapter 45: Writing Equations in PointSlope Form
Get Full SolutionsChapter 45: Writing Equations in PointSlope Form includes 69 full stepbystep solutions. Since 69 problems in chapter 45: Writing Equations in PointSlope Form have been answered, more than 34506 students have viewed full stepbystep solutions from this chapter. Algebra 1, Student Edition (MERRILL ALGEBRA 1) was written by and is associated to the ISBN: 9780078738227. 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.

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.

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

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

Fundamental Theorem.
The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n  r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

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.

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

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

Norm
IIA II. The ".e 2 norm" of A is the maximum ratio II Ax II/l1x II = O"max· Then II Ax II < IIAllllxll and IIABII < IIAIIIIBII and IIA + BII < IIAII + IIBII. Frobenius norm IIAII} = L La~. The.e 1 and.e oo norms are largest column and row sums of laij I.

Normal equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)·(b  Ax) = o.

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

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

Polar decomposition A = Q H.
Orthogonal Q times positive (semi)definite H.

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

Rotation matrix
R = [~ CS ] rotates the plane by () and R 1 = RT rotates back by (). Eigenvalues are eiO and eiO , eigenvectors are (1, ±i). c, s = cos (), sin ().

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

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.

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

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.