Question

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

Answer 1

do you know how to find the perpendicular slope ?

Answer 2

i subtract 2x from both sides?

Answer 3

like i l get -3y=2x+6

Answer 4

yep now you have to divide -3 both sides and you will get you "slope" = 2/3 now we need to find the perpendicular slope which is easy all you have to do is flip the bottom number with the top number and then multiply it by -1 i.e so now we know the slope we can plug imformation into slope-intercept formula which is \[y - y_{1} = m (x-x_{1})\] so lets plug in all the imfomation we know.
the line has to go through the coordinates (-2,-3) so lets plug that into our formula and we will have \[y + 3 = m(x+2)\] since we are looking we a perpendicular line we must plug in the perpendicular slope which is -3/2 so:\[y + 3 = -\frac{3}{2} (x+2)\]now just solve for y :\[y + 3= -\frac{3}{2}x - \frac{6}{2}\]\[y = -\frac{3}{2}x-\frac{6}{2}-3 = -\frac{3}{2} - 6\] so our final answer will be : \[y =-\frac{3}{2}x - 6\] i hoped this helped let me know if you have any questions