Question

Which function has the greatest rate of change?

Answer 1

Rate of change is the slope.

6x - 7y = 21

Convert to slope-intercept form(y = mx + b):

Subtract 6x to both sides:

-7y = -6x + 21

Divide -7 to both sides:

y = 6/7x - 3

Now it's in the form of y = mx + b, where 'm' is the slope. So the slope here is 6/7.

y = 2x - 2

This is already in slope-intercept form, so the slope here is 2.

For function C, take any two points and plug them into the slope equation.

m = y2-y1/x2-x1

(2, 7)
(3, 1)

m = (1 - 7)/(3 - 2)

m = -6/1

m = -6

So the slope of function C is -6.

(1, 2) and (-1, -4)

m = y2-y1/x2-x1

m = (-4 - 2)(/(-1 - 1)

m = -6/-2

m = 3

So function D has the highest rate of change.

*** Function C and D information based on the comments below ***