how do you put the points (-3,8) and (5,-7) into an equation in standard form?

use the two-point form and then rearrange

(y-8)/(x+3) = (-7-8)/(5+3) = -15/8
y-8 = -15/8 (x+3)
8(y-8) = -15(x+3)
8y-64 = -15x - 45
15x + 8y - 19 = 0