Question

If the line passing through the points
(a, 1) and (−2, 8)
is parallel to the line passing through the points
(12, 5) and (a + 2, 1),
what is the value of a?
a =

Answer 1

the slopes must be the same, so

(8-1)/(-2-a) = (1-5)/(a+2-12)
-7/(a+2) = -4/(a-10)
7(a-10) = 4(a+2)
7a-70 = 4a+8
3a = 78
a = 26

Answer 2

Since the lines are parallel this means the slopes are the same.

You then use y2-y1 (slope formula)
_____
x2-x1
and plug in both sets of points, (cross multipy) getting you

7(a-10)=-4(-2-a)
7a-70=8+4a
7a-4a=8+70
3a=78
a=26