Equation in slope intercept form for line through

Question

(1/4 , -1/2) & (3/4 , 6)

Answer 1

y - 6 = (6- - 1/2)/(3/4 - 1/4))(x- 3/4) in point slope form for (1/4, -1/2), (3/4, 6)

slope = (13/2)/(1/2) = 13, y intercept = -1/2 - 13/4 = -15/4

y = 13x -39/4 +6

y = 13x -15/4 in slope intercept form

check the answer plug in the points

13(1/4)-15/4 = -2/4 = -1/2

13(3/4) -15/4 = 24/4 = 6 they work