Find the slope and y-intercept of the line is perpendicular to y = 3x - 3 and passes through the point (-8,-2)

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.

Slope -1/3  y intercept -14/3