Rate of Change is the same as Slope.
A.
[tex]\sf14x-2y=8[/tex]
Convert to slope-intercept form.
Subtract 14x to both sides:
[tex]\sf-2y=-14x+8[/tex]
Divide -2 to both sides:
[tex]\sf~y=7x-4[/tex]
So the rate of change here is 7.
B.
[tex]\sf~y=6x-5[/tex]
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
[tex]\sf~m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Plug in the numbers:
[tex]\sf~m=\dfrac{3-(-2)}{0-(-1)}[/tex]
Subtract:
[tex]\sf~m=\dfrac{5}{1}[/tex]
Divide:
[tex]\sf~m=5[/tex]
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
[tex]\sf~m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Plug in the numbers:
[tex]\sf~m=\dfrac{3-(-2)}{1-0}[/tex]
Subtract:
[tex]\sf~m=\dfrac{5}{1}[/tex]
Divide:
[tex]\sf~m=5[/tex]
So the rate of change here is 5.
Therefore, A has the greatest rate of change.
