What is the value of a such that (−2, 1) and (0, a) lie on a line parallel to the line passing through points (5, 7) and (7, 4)?

Answer 1

(5,7) (7,4) m = 4-7/7-5 =-3/2 This is the slope of the line with points (5,7) (7,4). We will call this line 1.

Since the lines are parallel ,the slope of the second line must also be -3/2.

-3/2= a-1/0+2 set the slope of the first line equal to the points of the second line and cross multiply to solve.

2(a-1)= -3(0+2)

Solve for a and you will find the y value needed for the ungiven point.

Answer 2

I thought I'd provide a different solution than most will provide.

Note that 7 - 5 = 2, as does 0 - -2 (the first coordinates of each pair)

Thus, a - 1 = 4 - 7

a = 4 - 7 + 1 = -2