What is the slope of the line represented by the equation 2x+3y= –12 ? –32

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A line that has perpendicular slope will have a product of -1 when multiplied by the slope of another line.

First, find the slope of the given line in the equation:

2x + 3y = 6
Solve for y:
Subtract 2x from both sides, then divide by 3
3y = 6–2x
y = 3-(2/3)x, or y = -(2/3)x+3

The slope is -2/3, so the product of the perpendicular slope and this slope must equal -1. How to find it? Easy: just flip the equation and get rid of the - sign to get:
3/2

-(2/3)*3/2 = (-2*3)/(3*2) = -6/6 = -1

Bam! So the slope of the perpendicular line is 3/2