Question

Which representation has the same rate of change of y with respect to x as the equation x + 2y = 6?
A
y = −1 over 2x + 2
B
y. x
C
x. y. negative 15, negative 0.5, negative 10, negative 3, negative 5, negative 5.5, 0, negative 8, 5, negative 10.5, 10, negative 13
D
All of the above

Answer 1

x + 2y = 6 -> 2y = −x + 6 -> y = (−1/2)x + 3, so the slope (rate of change) is −1/2.

A: y = (−1/2)x + 2 has slope −1/2.
C: The table (x, y) = (−15, −0.5), (−10, −3), (−5, −5.5), (0, −8), (5, −10.5), (10, −13) gives slopes between consecutive points (Δy/Δx) = (−2.5)/5 = −1/2, so slope −1/2.

Thus all representations shown have the same rate of change. Answer: D.