Precalculus Examples

$(- 3, 3.6)$ , $(5, 2)$

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.

$m = \frac{2 - (3.6)}{5 - (- 3)}$

Step 5

Simplify.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Multiply $- 1$ by $3.6$ .

$m = \frac{2 - 3.6}{5 - (- 3)}$

Step 5.1.2

Subtract $3.6$ from $2$ .

$m = \frac{- 1.6}{5 - (- 3)}$

Step 5.2

Simplify the denominator.

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Step 5.2.1

Multiply $- 1$ by $- 3$ .

$m = \frac{- 1.6}{5 + 3}$

Step 5.2.2

Add $5$ and $3$ .

$m = \frac{- 1.6}{8}$

Step 5.3

Divide $- 1.6$ by $8$ .

$m = - 0.2$

Step 6