If the line passing through the points (a, 1) and (5, 7) is parallel to the line passing through the points (8, 8) and (a + 2, 1), what is the value of a?
a = ?
slope of 1st line is (7-1)/(5-a) = 6/(5-a)
slope of 2nd line is (1-8)/(a+2-8) = -7/(a-6)
If the lines are parallel, the slopes are equal, so
6/(5-a) = -7/(a-6)
6(a-6) = -7(5-a)
6a-36 = 7a-35
-a = 1
a = -1