Answer:
5x -3y = 15
Step-by-step explanation:
First find the slope of the line through ( -3,2) and (2,-1)
m = (y2-y1)/(x2-x1)
=( -1-2)/(2--3)
= -3/(2+3)
= -3/5
We want a line that is perpendicular so the slopes will multiply to -1
m * -3/5 = -1
Multiply each side by -5/3
m * -3/5 * -5/3 = -1 *-5/3
m = 5/3
The slope of the perpendicular line is 5/3
We have a slope and a point
Using point slope form
y-y1 = m(x-x1)
y-0 = 5/3( x-3)
y = 5/3( x-3)
Distribute
y = 5/3x -5
Multiply each side by 3
3*y = 3(5/3x -5)
3y = 5x - 15
Subtract 5x from each side
-5x+3y = -15
Multiply each side by -1
5x -3y = 15
