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.
