Examples

$y = x - 2$ ,

$(- 3, - 5)$ ,

$(5, 3)$

Step 1

Write

$y = x - 2$ as a function.

$f (x) = x - 2$

Step 2

Substitute using the average rate of change formula.

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Step 2.1

The average rate of change of a function can be found by calculating the change in

$y$ values of the two points divided by the change in

$x$ values of the two points.

$\frac{f (5) - f (- 3)}{(5) - (- 3)}$

Step 2.2

Substitute the equation

$y = x - 2$ for

$f (5)$ and

$f (- 3)$ , replacing

$x$ in the function with the corresponding

$x$ value.

$\frac{((5) - 2) - ((- 3) - 2)}{(5) - (- 3)}$

Step 3

Simplify the expression.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Subtract

$2$ from

$- 3$ .

$\frac{5 - 2 - - 5}{5 - (- 3)}$

Step 3.1.2

Multiply

$- 1$ by

$- 5$ .

$\frac{5 - 2 + 5}{5 - (- 3)}$

Step 3.1.3

Subtract

$2$ from

$5$ .

$\frac{3 + 5}{5 - (- 3)}$

Step 3.1.4

Add

$3$ and

$5$ .

$\frac{8}{5 - (- 3)}$

Step 3.2

Simplify the denominator.

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Step 3.2.1

Multiply

$- 1$ by

$- 3$ .

$\frac{8}{5 + 3}$

Step 3.2.2

Add

$5$ and

$3$ .

$\frac{8}{8}$

Step 3.3

Divide

$8$ by

$8$ .

$1$

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