Question

Choose the equation of the line passing through the point (-4, -2) and perpendicular to y = -x + 6.
y = -x + 6

y = x - 6

y = -x - 2

y = x + 2

Answer 1

What is the slope of \(y=-x+6\)?

Answer 2

-x

Answer 3

The slope is the coefficient of the \(x\) term, not the \(x\) term itself.

Answer 4

Then -1, I think

Answer 5

Right. What's the slope of a perpendicular line relative to a given line? If I have a line with a slope of \(\dfrac{a}{b}\), what is the slope of a line perpendicular to this one?

Answer 6

b/a

Answer 7

\(\bf \cfrac{a}{{\color{blue}{ b}}}\qquad negative\to -\cfrac{a}{{\color{blue}{ b}}}\qquad reciprocal\to -\cfrac{{\color{blue}{ b}}}{a}\)

Answer 8

I know

Answer 9

Okay, so the slope would in fact be \(-\dfrac{b}{a}\), not \(\dfrac{b}{a}\). So now if the slope of \(y=-x+6\) is -1, what's the slope of a perpendicular line?

Answer 10

It would be -B / A, correct?

Answer 11

If \(\dfrac{a}{b}=-1\), what's \(-\dfrac{b}{a}\)?

Answer 12

1?

Answer 13

\(\bf -1\to -\cfrac{1}{{\color{blue}{ 1}}}\qquad negative\to +\cfrac{1}{{\color{blue}{ 1}}}\qquad reciprocal\to +\cfrac{{\color{blue}{ 1}}}{1}\to 1\)

Answer 14

Yes. Now, using the point-slope formula for a line, you would plug in the given point (-4,-2) and the slope 1:
\[y-y_0=m(x-x_0)\]

Answer 15

Would the answer be D?

Answer 16

?