Question

For which value of a are the graphs of –4 = 3x + 6y and ax – 8y = 12 parallel?

a = –4
a =
a =
a = 2

Answer 1

Put both equations into slope-intercept form (y = mx + b).

First: -4 = 3x + 6y → 6y = -3x - 4 → y = (-3/6)x - 4/6 = (-1/2)x - 2/3, so slope m1 = -1/2.

Second: ax - 8y = 12 → 8y = ax - 12 → y = (a/8)x - 12/8, so slope m2 = a/8.

For parallel lines set m1 = m2: a/8 = -1/2 → a = 8·(-1/2) = -4.

Answer: a = -4.