Step 1: Find the equation of the line that passes through (-2,3) and (2, -3).
The slope of this line will be
m = (-3 - 3)/(2 - (-2))
m = -6/4
The equation is y = -(6/4)x + b
We must find the y-intercept of equation by substituting values from any of these points. Lets pick (-2,3).
3 = -(6/4)(-2) + b
3 = 3 +b
0 = b
Our equation of the line that passes through both of these points is y = -(6/4)x
Step 2: Find the slope of the line that is perpendicular to the line from previous answer and passes through (3,2).
Perpendicular slopes have negative reciprocals. This means the slope of the line that passes through (3,2) is
4/6 = 2/3