 44.1: Write an equation of the line that passes through each point with t...
 44.2: Write an equation of the line that passes through each point with t...
 44.3: Write an equation of the line that passes through each point with t...
 44.4: Write an equation of the line that passes through each pair of points.
 44.5: Write an equation of the line that passes through each pair of points.
 44.6: Write an equation of the line that passes through each pair of points.
 44.7: STANDARDIZED TEST PRACTICE The table of ordered x y 5 2 0 7 pairs ...
 44.8: CANOE RENTAL For Exercises 8 and 9, use the information at the righ...
 44.9: CANOE RENTAL For Exercises 8 and 9, use the information at the righ...
 44.10: Write an equation of the line that passes through each point with t...
 44.11: Write an equation of the line that passes through each point with t...
 44.12: Write an equation of the line that passes through each point with t...
 44.13: Write an equation of the line that passes through each point with t...
 44.14: Write an equation of the line that passes through each point with t...
 44.15: Write an equation of the line that passes through each point with t...
 44.16: Write an equation of the line that passes through each point with t...
 44.17: Write an equation of the line that passes through each point with t...
 44.18: Write an equation of the line that passes through each pair of points.
 44.19: Write an equation of the line that passes through each pair of points.
 44.20: Write an equation of the line that passes through each pair of points.
 44.21: Write an equation of the line that passes through each pair of points.
 44.22: Write an equation of the line that passes through each pair of points.
 44.23: Write an equation of the line that passes through each pair of points.
 44.24: Write an equation of the line that passes through each pair of points.
 44.25: Write an equation of the line that passes through each pair of points.
 44.26: POPULATION For Exercises 26 and 27, use the data at the top of page...
 44.27: POPULATION For Exercises 26 and 27, use the data at the top of page...
 44.28: DOGS For Exercises 28 and 29, refer to the information below.
 44.29: DOGS For Exercises 28 and 29, refer to the information below.
 44.30: Write an equation of the line that passes through each pair of points.
 44.31: Write an equation of the line that passes through each pair of points.
 44.32: Write an equation of the line that passes through each pair of points.
 44.33: Write an equation of the line that has an xintercept 3 and a yin...
 44.34: For Exercises 34 and 35, consider line that passes through (14, 2) ...
 44.35: For Exercises 34 and 35, consider line that passes through (14, 2) ...
 44.36: CHALLENGE The xintercept of a line is p, and the yintercept is q....
 44.37: OPEN ENDED Create a realworld situation that fits the graph at the...
 44.38: REASONING Tell whether the statement is sometimes, always, or never...
 44.39: Writing in Math Use the information about population on page 213 to...
 44.40: Which equation best describes the relationship between the values o...
 44.41: REVIEW Mrs. Aguilars bedroom is shaped like a rectangle that measur...
 44.42: Graph each equation.
 44.43: Graph each equation.
 44.44: Graph each equation.
 44.45: HEALTH Each time your heart beats, it pumps 2.5 ounces of blood. Wr...
 44.46: Determine the xintercept and yintercept of each linear function a...
 44.47: Determine the xintercept and yintercept of each linear function a...
 44.48: Determine the domain and range of each relation.
 44.49: Determine the domain and range of each relation.
 44.50: PREREQUISITE SKILL Find each difference.
 44.51: PREREQUISITE SKILL Find each difference.
 44.52: PREREQUISITE SKILL Find each difference.
 44.53: PREREQUISITE SKILL Find each difference.
Solutions for Chapter 44: Writing Equations in SlopeIntercept Form
Full solutions for Algebra 1, Student Edition (MERRILL ALGEBRA 1)  1st Edition
ISBN: 9780078738227
Solutions for Chapter 44: Writing Equations in SlopeIntercept Form
Get Full SolutionsChapter 44: Writing Equations in SlopeIntercept Form includes 53 full stepbystep solutions. Since 53 problems in chapter 44: Writing Equations in SlopeIntercept Form have been answered, more than 35277 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 expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Algebra 1, Student Edition (MERRILL ALGEBRA 1) , edition: 1.

Back substitution.
Upper triangular systems are solved in reverse order Xn to Xl.

Change of basis matrix M.
The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

Complete solution x = x p + Xn to Ax = b.
(Particular x p) + (x n in nullspace).

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.

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

Fibonacci numbers
0,1,1,2,3,5, ... satisfy Fn = Fnl + Fn 2 = (A7 A~)I()q A2). Growth rate Al = (1 + .J5) 12 is the largest eigenvalue of the Fibonacci matrix [ } A].

GramSchmidt orthogonalization A = QR.
Independent columns in A, orthonormal columns in Q. Each column q j of Q is a combination of the first j columns of A (and conversely, so R is upper triangular). Convention: diag(R) > o.

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

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

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

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

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

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

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).

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

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

Simplex method for linear programming.
The minimum cost vector x * is found by moving from comer to lower cost comer along the edges of the feasible set (where the constraints Ax = b and x > 0 are satisfied). Minimum cost at a comer!

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

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

Symmetric matrix A.
The transpose is AT = A, and aU = a ji. AI is also symmetric.