Which function has the greatest rate of change?

A.

6x - 7y = 21

B.

y = 2x - 2

C.

x y

2 7

3 13

4 19

For an equation expressed as Ax + By + C, the rate of change is equal to - A/B. For the first equation, it is 6/7. For the second equation, the slope is 2. Then for the third equation, m = (19 - 7) / (4 - 2) = 6. Thus, the greatest slope is in third choice.

The rate of change is the slope ... and in y = mx + b form, the slope is in the m position. So we need to put the equations in y = mx + b form.

A. 6x - 7y = 21

-7y = - 6x + 21

y = 6/7x - 2 ... so the slope here is 6/7 or 0.857

B. y = 2x - 2 ... this is already in the form we need ... the slope is 2

C. (2,7) (3,13)

slope = (13-7) / (3-2) = 6/1 or just 6

the slope with the greatest rate of change is gonna be the one with the highest slope ... and that would be C.