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MATH / The following line is parameterized, so that its direction vector is of the form…

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problem

The following line is parameterized, so that its direction vector is of the form $\begin{pmatrix} -7 \\ b \end{pmatrix}.$ Find b.b. [asy] unitsize(0.4 cm); pair A, B, L, R; int i, n; for (i = -8; i <= 8; ++i) { draw((i,-8)--(i,8),gray(0.7)); draw((-8,i)--(8,i),gray(0.7)); } draw((-8,0)--(8,0),Arrows(6)); draw((0,-8)--(0,8),Arrows(6)); A = (-5,4); B = (-1,3); L = extension(A, B, (-8,0), (-8,1)); R = extension(A, B, (8,0), (8,1)); draw(L--R, red); label("xx", (8,0), E); label("yy", (0,8), N); [/asy]
Plain-text mathematical notation (without MathML)
The following line is parameterized, so that its direction vector is of the form $\begin{pmatrix} -7 \\ b \end{pmatrix}.$  Find b.

[asy]
unitsize(0.4 cm);

pair A, B, L, R;
int i, n;

for (i = -8; i <= 8; ++i) {
  draw((i,-8)--(i,8),gray(0.7));
  draw((-8,i)--(8,i),gray(0.7));
}

draw((-8,0)--(8,0),Arrows(6));
draw((0,-8)--(0,8),Arrows(6));

A = (-5,4);
B = (-1,3);
L = extension(A, B, (-8,0), (-8,1));
R = extension(A, B, (8,0), (8,1));

draw(L--R, red);

label("x", (8,0), E);
label("y", (0,8), N);
[/asy]
Original LaTeX notation
The following line is parameterized, so that its direction vector is of the form $\begin{pmatrix} -7 \\ b \end{pmatrix}.$  Find $b.$

[asy]
unitsize(0.4 cm);

pair A, B, L, R;
int i, n;

for (i = -8; i <= 8; ++i) {
  draw((i,-8)--(i,8),gray(0.7));
  draw((-8,i)--(8,i),gray(0.7));
}

draw((-8,0)--(8,0),Arrows(6));
draw((0,-8)--(0,8),Arrows(6));

A = (-5,4);
B = (-1,3);
L = extension(A, B, (-8,0), (-8,1));
R = extension(A, B, (8,0), (8,1));

draw(L--R, red);

label("$x$", (8,0), E);
label("$y$", (0,8), N);
[/asy]

level

Level 3

type

Precalculus

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Source and history

task_id
59d648c9-06bb-5e05-addf-ca69949b9e7a
task_key
precalculus--test--59d648c9-06bb-5e05-addf-ca69949b9e7a
task_revision_id
1
config / split
precalculus / test

Official source

initial import