Question

A line passes through (2, -1) and (8, 4).

Answer 1

Slope of the line = (4--1) / (8-2)  = 5/6

point slope form is  y-y1 = m(x-x1)  where m=slope and (x1,y1) is a point on the line 
so the answer to (a) is    y + 1 = (5/6)(x - 2)  Answer

(b)  multiply the above equation by 6:-

6y + 6  = 5(x - 2)

6y + 6 = 5x - 10

5x - 6y  = 16    is the equation in standard form  Answer