Precalculus Examples

$(- 1, - 6)$ and $(- 5, 2)$

Step 1

To find the average rate of change, find the slope.

Step 2

Slope is equal to the change in $y$ over the change in $x$ , or rise over run.

$m = \frac{change in y}{change in x}$

Step 3

The change in $x$ is equal to the difference in x-coordinates (also called run), and the change in $y$ is equal to the difference in y-coordinates (also called rise).

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

Step 4

Substitute in the values of $x$ and $y$ into the equation to find the slope.

$m = \frac{2 - (- 6)}{- 5 - (- 1)}$

Step 5

Simplify.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Multiply $- 1$ by $- 6$ .

$m = \frac{2 + 6}{- 5 - (- 1)}$

Step 5.1.2

Add $2$ and $6$ .

$m = \frac{8}{- 5 - (- 1)}$

Step 5.2

Simplify the denominator.

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Step 5.2.1

Multiply $- 1$ by $- 1$ .

$m = \frac{8}{- 5 + 1}$

Step 5.2.2

Add $- 5$ and $1$ .

$m = \frac{8}{- 4}$

Step 5.3

Divide $8$ by $- 4$ .

$m = - 2$

Step 6