Question

Help meh PleAse

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

$\sf~m=\dfrac{y_2-y_1}{x_2-x_1}$

Plug in the numbers:

$\sf~m=\dfrac{3-(-2)}{0-(-1)}$

Subtract:

$\sf~m=\dfrac{5}{1}$

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

$\sf~m=\dfrac{y_2-y_1}{x_2-x_1}$

Plug in the numbers:

$\sf~m=\dfrac{3-(-2)}{1-0}$

Subtract:

$\sf~m=\dfrac{5}{1}$

Divide:

$\sf~m=5$

So the rate of change here is 5.

Therefore, A has the greatest rate of change.