Question

Which of the following is true about the relationship between the slopes of the lines whose equations are 8x - 9y = 5 and 9x - 8y = 1?

They are equal.
They are reciprocals.
They are opposites.

Answer 1

reciprocals, but not negative reciprocals

Explanation:

8x - 9y = 5

9y = 8x - 5

y = 8/9x - 5/9

m1 = 8/9

9x - 8y = 1

8y = 9x - 1

y = 9/8x - 1/8

m2 = 9/8

Answer 2

reciprocals

Explanation:

Let's actually find the slopes. Then we can better compare them.

8x - 9y = 5 → - 9y = 5 - 8x → slope is m = (-8) / (-9), or 8/9.

9x - 8y = 1 → - 8y = 1 - 9x → slope is (-9) / (-8), or 9/8

These two slopes are reciprocals (but not negative reciprocals).