Precalculus Examples

$\begin{array}{c} x & y \\ 1 & 1 \\ 2 & 2 \\ 3 & 3 \end{array}$

Step 1

Choose the starting and ending values from the table.

$(1, 1), (3, 3)$

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.

$m = \frac{3 - (1)}{3 - (1)}$

Step 6

Cancel the common factor of $3 - (1)$ .

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Step 6.1

Cancel the common factor.

$m = \frac{3 - (1)}{3 - (1)}$

Step 6.2

Rewrite the expression.

$m = 1$

Step 7