Examples

y = 9 - 5 x

$y = 9 - 5 x$ ,

(1, 4)

$(1, 4)$ ,

(- 1, 14)

$(- 1, 14)$

Step 1

Write

y = 9 - 5 x

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

f (x) = 9 - 5 x

$f (x) = 9 - 5 x$

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

$y$ values of the two points divided by the change in

x

$x$ values of the two points.

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

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

Step 2.2

Substitute the equation

y = 9 - 5 x

$y = 9 - 5 x$ for

f (1)

$f (1)$ and

f (- 1)

$f (- 1)$ , replacing

x

$x$ in the function with the corresponding

x

$x$ value.

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

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

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

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

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

$- 5$ by

1

$1$ .

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

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

Step 3.1.2

Multiply

- 5

$- 5$ by

- 1

$- 1$ .

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

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

Step 3.1.3

Add

9

$9$ and

5

$5$ .

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

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

Step 3.1.4

Multiply

- 1

$- 1$ by

14

$14$ .

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

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

Step 3.1.5

Subtract

5

$5$ from

9

$9$ .

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

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

Step 3.1.6

Subtract

14

$14$ from

4

$4$ .

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

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

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

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

Step 3.2

Simplify the denominator.

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Step 3.2.1

Multiply

- 1

$- 1$ by

- 1

$- 1$ .

\frac{- 10}{1 + 1}

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

Step 3.2.2

Add

1

$1$ and

1

$1$ .

\frac{- 10}{2}

$\frac{- 10}{2}$

\frac{- 10}{2}

$\frac{- 10}{2}$

Step 3.3

Divide

- 10

$- 10$ by

2

$2$ .

- 5

$- 5$

- 5

$- 5$

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