Question

The equation of the line the point (-1,3) and perpendicular to the line x+2y=-6 is

Answer 1

Do you know slope intercept form?

Answer 2

y= mx+b

Answer 3

You want to find the slop of the line \(x+2y=-6\), so you need to put it in slope intercept form.

Answer 4

how do i do that

Answer 5

Do you know how to isolate a variable?

Answer 6

If you isolate y, then you will be in slope intercept form.

Answer 7

no i do not

Answer 8

So you don't know how to solve for y?

Answer 9

can you show me

Answer 10

Okay if you start with \[
x+2y=-6
\]The first thing you wanna do to isolate \(y\) is to get the other terms on the other side of the equation by subtracting them.. In this case, the other term is \(x\). So to get rid of it, we subtract \(x\) from both sides.\[
x+2y - x = -6 -x
\]Now the \(x\) and \(-x\) will cancel out.\[
x-x+2y \rightarrow 2y
\]The result is \[
2y=-6-x
\]

Answer 11

But \(y\) is still not isolated because is has the coefficient \(2\) in front of it. To get rid of that, we have to divide both sides by 2.\[
\frac{2y}{2}= \frac{-6-x}{2}
\]This simplifies as follows \[
y = -3-\frac{x}{2}
\]

Answer 12

Are you familiar with this process at all?

Answer 13

so i would have to subtrat -6 from -x right

Answer 14

Subtract \(-6\) from \(-x\)? We are solving for \(y\), not for \(x\).

Answer 15

oh okay no im not fimilar with this process

Answer 16

y=-3-x/2 how do we solve that

Answer 17

Anyway, we have the following equation \[
y = -\frac{1}{2}x-3
\]Compare it to \[
y=mx+b
\]This means \(m=-1/2\) and \(b=-3\)

Answer 18

These are the same:\[-\frac{x}{2} = -\frac{1}{2}x\]

Answer 19

But we're not done yet. We still need to find a perpendicular line.

Answer 20

so the final answer is x-2y=3

Answer 21

No

Answer 22

To find a perpendicular line, we use the other slope. Since the slope of the other line is \(-1/2\), then our line must have a slop of \(2\), because that is the opposite of the reciprocal of \(-1/2\)

Answer 23

So we know the line we're looking for is of the form \[
y=2x+b

\]But we need to find out what \(b\) is.

Answer 24

It must intersect with the point \((-1,3)\). So we plug it in \[
(3) = 2(-1)+b
\]Now we have enough information to solve for \(b\).

Answer 25

so 2*-2+b