finding missing value in parallel lines

Question

if the line passing through the points (1,a) and (4,-2) is parallel to the line passing through the points (2,8) and (-7, a+4), what is the value of a?

Answer 1

Parallel lines slopes are equal.

First line points (1,a) and (4,-2)

Slope of the first line is m1 = -2-a/4-1

m1 = -2-a/3

Second line points are (2,8) and (-7,a+4)

Slope of the second line is m2 = a+4-8/-7-2

m2 = a-4/-9

There fore -2-a/3 = a-4/-9

-9(-2-a) = 3(a-4)

+18+9a = 3a-12

18+9a-3a+12 = 0

6a+30 = 0

6a =-30

a = -30/6

a = -5

The value of a = -5.