Precalculus Examples

$\begin{array}{c} t & B \\ 4.5 & 45.5 \\ 8 & 21 \\ 10 & 7 \end{array}$

Step 1

Choose the starting and ending values from the table.

$(4.5, 45.5), (10, 7)$

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.

$m = \frac{7 - (45.5)}{10 - (4.5)}$

Step 6

Simplify.

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Step 6.1

Simplify the numerator.

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Step 6.1.1

Multiply $- 1$ by $45.5$ .

$m = \frac{7 - 45.5}{10 - (4.5)}$

Step 6.1.2

Subtract $45.5$ from $7$ .

$m = \frac{- 38.5}{10 - (4.5)}$

Step 6.2

Simplify the denominator.

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Step 6.2.1

Multiply $- 1$ by $4.5$ .

$m = \frac{- 38.5}{10 - 4.5}$

Step 6.2.2

Subtract $4.5$ from $10$ .

$m = \frac{- 38.5}{5.5}$

Step 6.3

Divide $- 38.5$ by $5.5$ .

$m = - 7$

Step 7