3x - 2y = 12
- 2y= - 3x + 12
y = 3/2x - 6
Slope of your line is 3/2 so the slope of the perpendicular line is its opposite reciprocal, - 2/3.
y = - 2/3x + b
Plug in your given point and solve for b.
- 8 = -2/3(6) + b
- 8 = - 4 + b
- 4 = b
Your equation of the perpendicular line that goes through point (6, - 8) is y = - 2/3x - 4.
This is all assuming your original equation is 3x - 2y = 12 like user AlizaR asked.
