Examples

$y = 9 - 5 x$ , $(1, 4)$ , $(- 1, 14)$

Step 1

Write $y = 9 - 5 x$ as a function.

$f (x) = 9 - 5 x$

Step 2

Substitute using the average rate of change formula.

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Step 2.1

The average rate of change of a function can be found by calculating the change in $y$ values of the two points divided by the change in $x$ values of the two points.

$\frac{f (1) - f (- 1)}{(1) - (- 1)}$

Step 2.2

Substitute the equation $y = 9 - 5 x$ for $f (1)$ and $f (- 1)$ , replacing $x$ in the function with the corresponding $x$ value.

$\frac{(9 - 5 \cdot 1) - (9 - 5 \cdot - 1)}{(1) - (- 1)}$

Step 3

Simplify the expression.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Multiply $- 5$ by $1$ .

$\frac{9 - 5 - (9 - 5 \cdot - 1)}{1 - (- 1)}$

Step 3.1.2

Multiply $- 5$ by $- 1$ .

$\frac{9 - 5 - (9 + 5)}{1 - (- 1)}$

Step 3.1.3

Add $9$ and $5$ .

$\frac{9 - 5 - 1 \cdot 14}{1 - (- 1)}$

Step 3.1.4

Multiply $- 1$ by $14$ .

$\frac{9 - 5 - 14}{1 - (- 1)}$

Step 3.1.5

Subtract $5$ from $9$ .

$\frac{4 - 14}{1 - (- 1)}$

Step 3.1.6

Subtract $14$ from $4$ .

$\frac{- 10}{1 - (- 1)}$

Step 3.2

Simplify the denominator.

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Step 3.2.1

Multiply $- 1$ by $- 1$ .

$\frac{- 10}{1 + 1}$

Step 3.2.2

Add $1$ and $1$ .

$\frac{- 10}{2}$

Step 3.3

Divide $- 10$ by $2$ .

$- 5$

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