Question

for what values of p are (8,1) (3,-2p) (p,-5) collinear.

Answer 1

The equation of the line joining the first two points,
(y-1) = {(-2p-1)/(-5)} ( x - 8)
⇒ -5y + 5 = -2px + 16p - x + 8
(You may simplify it)

Then, put (p,-5) in the equation;
25 + 5 = -2p² + 16p - p + 8
⇒ 2p² -15p + 22 = 0
⇒ 2p² - 4p - 11p +22 = 0
⇒2p(p-2) - 11(p-2) = 0
⇒(p-2)(2p-11) = 0
Therefore, p=2, 11/2

Answer 2

hope you have understand it .
p is 11/2 or 2