Which is the equation for the line perpendicular to y = –5/3 x + 11 1/3 and containing p(–2, 3)?
i have been trying really hard but i want to make sure i know how to do this right. explain the steps and their purposes thoroughly so i can understand it.

Okay, to answer this question, 
Perpendicular lines have slopes that are inverse of one another and with opposite signs so, 
If a line has a slope of m= -2 than a perpendicular line will have slope m=1/2
If a line has a slope of m= -3/4 than a perpendicular line will have slope m=4/3 If a line has a slope of m= 6 than a perpendicular line will have slope m=-1/6

So, just find the slope of your line, using it, get the slope of the line that will be perpendicular and then just get the equation for a line that has that slope and passes through point (-2,3) using: y - y1 = m(x - x1)
I hope I helped you with my answer