Precalculus Examples

$\begin{array}{c} x & y \\ - 2 & 3 \\ - 1 & 5 \\ 0 & 7 \\ 1 & 9 \\ 2 & 11 \end{array}$

Step 1

Choose the starting and ending values from the table.

$(- 2, 3), (2, 11)$

Step 2

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

Step 3

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 4

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 5

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

$m = \frac{11 - (3)}{2 - (- 2)}$

Step 6

Simplify.

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Step 6.1

Simplify the numerator.

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Step 6.1.1

Multiply $- 1$ by $3$ .

$m = \frac{11 - 3}{2 - (- 2)}$

Step 6.1.2

Subtract $3$ from $11$ .

$m = \frac{8}{2 - (- 2)}$

Step 6.2

Simplify the denominator.

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Step 6.2.1

Multiply $- 1$ by $- 2$ .

$m = \frac{8}{2 + 2}$

Step 6.2.2

Add $2$ and $2$ .

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

Step 6.3

Divide $8$ by $4$ .

$m = 2$

Step 7