Precalculus Examples

$(- 2, 4)$ to $(1, - 5)$

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.

$m = \frac{- 5 - (4)}{1 - (- 2)}$

Step 5

Simplify.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Multiply $- 1$ by $4$ .

$m = \frac{- 5 - 4}{1 - (- 2)}$

Step 5.1.2

Subtract $4$ from $- 5$ .

$m = \frac{- 9}{1 - (- 2)}$

Step 5.2

Simplify the denominator.

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Step 5.2.1

Multiply $- 1$ by $- 2$ .

$m = \frac{- 9}{1 + 2}$

Step 5.2.2

Add $1$ and $2$ .

$m = \frac{- 9}{3}$

Step 5.3

Divide $- 9$ by $3$ .

$m = - 3$

Step 6