Write an equation of the line that passes through (-3, 3) and is perpendicular to the line 2y = 8x - 6.

My method is not the most common, but is correct:

Realize that if 2 lines are perpendicular, then the slope of one (call it "m") is the negative reciprocal of the slope of the other.

Solving 2y = 8x - 6 for y:  y = 4x - 3.  This has a slope of "m"=4, and so the slope of any line perpendicular to y = 4x - 3  will be -1/4.

Now we have the slope of the new line and know that this line passes through (-3,3).  Use the point-slope formula here:

y-3 = (-1/4)(x-[-3]), or     y-3 = (-1/4)(x+3)