Let's do it in standard form then convert to slope/intercept. Just for fun.
y = 3x - 3
3x - y = 3
The perpendicular family is gotten by swapping the coefficients on x and y, negating one of them.
x + 3y = some constant
We want to go through (-8,-2) so the constant must be
x + 3y = -8 + 3(-2) = -14
3y = -x - 14
y = (-1/3) x - 14/3
We see the slope is -1/3. We knew it had to be because we started with a slope of 3 and the perpendicular is the negative reciprocal.
We read the y intercept (what we get when x=0) off the slope intercept form of the line as -14/3.
Answer: Slope -1/3 y intercept -14/3
