What is the equation of the line that passes through (–2, –3) and is perpendicular to 2x – 3y = 6?

Question

austinl · Answer

Okay, are you familiar with slope-intercept form?

anonymous · Answer

I am.

anonymous · Answer

first you need to find the slope of the given equation. Can you do that ?

arabpride · Answer

u have to plug in the x coordinate into where it says 2x, then y coordinate to where it says -3y......nd work with that

austinl · Answer

Okay, I would first put it in that form. You essentially just solve for y.

austinl · Answer

And in doing so, you find the slope as well. The term that ends up in front of x.

anonymous · Answer

Not sure if I did this right, Y=(2/3)x-2?

austinl · Answer

$2x-3y=6$
$-3y=-2x+6$
$\displaystyle y=\frac{2}{3}x-2$

Good job, now what is the slope?

anonymous · Answer

(2/3)

austinl · Answer

Correct.
Now for a line to be perpendicular to another, it's slope is the negative reciprocal. Do you know how to do that?

anonymous · Answer

-(3/2) right?

austinl · Answer

Yes!

So now we have this basic equation.

$\displaystyle y=-\frac{3}{2}x+b$

We need to solve for b, do you know how we would do this?

austinl · Answer

I mean, figure out what b is. There is a difference :P

anonymous · Answer

I think I know the answer $$Y=-\frac{ 3 }{ 2 } x-6?$$

austinl · Answer

That is correct! Good job!