Question

Help meh PleAse

Which function has the greatest rate of change?

A. 14x – 2y = 8

B. y = 6x – 5

C.
x y
−2 −7
−1 −2
0 3
D.
The Graph is Letter D.

Answer 1

Rate of Change is the same as Slope.

A.


`\sf14x-2y=8`

Convert to slope-intercept form.

Subtract 14x to both sides:


`\sf-2y=-14x+8`

Divide -2 to both sides:


`\sf~y=7x-4`

So the rate of change here is 7.

B.


`\sf~y=6x-5`

This is already in slope-intercept form, so the rate of change here is 6.

C.

Take any two points on the graph and plug them into the slope formula.

Let's take (-1, -2) and (0, 3).
x1 y1 x2 y2


`\sf~m=(y_2-y_1)/(x_2-x_1)`

Plug in the numbers:


`\sf~m=(3-(-2))/(0-(-1))`

Subtract:


`\sf~m=(5)/(1)`

Divide:


`\sf~m=5`

So the rate of change here is 5.

D.

Take any two points on the line and plug them into the slope formula.

Let's take (0, -2) and (1, 3)
x1 y1 x2 y2


`\sf~m=(y_2-y_1)/(x_2-x_1)`

Plug in the numbers:


`\sf~m=(3-(-2))/(1-0)`

Subtract:


`\sf~m=(5)/(1)`

Divide:


`\sf~m=5`

So the rate of change here is 5.

Therefore, A has the greatest rate of change.