Precalculus Examples

$y = x - 9$ , $(0, - 9)$ , $(7, - 2)$

Step 1

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

$f (x) = x - 9$

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.

$\frac{f (7) - f (0)}{(7) - (0)}$

Step 2.2

Substitute the equation $y = x - 9$ for $f (7)$ and $f (0)$ , replacing $x$ in the function with the corresponding $x$ value.

$\frac{((7) - 9) - ((0) - 9)}{(7) - (0)}$

Step 3

Simplify the expression.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Subtract $9$ from $0$ .

$\frac{7 - 9 - - 9}{7 - (0)}$

Step 3.1.2

Multiply $- 1$ by $- 9$ .

$\frac{7 - 9 + 9}{7 - (0)}$

Step 3.1.3

Subtract $9$ from $7$ .

$\frac{- 2 + 9}{7 - (0)}$

Step 3.1.4

Add $- 2$ and $9$ .

$\frac{7}{7 - (0)}$

Step 3.2

Simplify the denominator.

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Step 3.2.1

Multiply $- 1$ by $0$ .

$\frac{7}{7 + 0}$

Step 3.2.2

Add $7$ and $0$ .

$\frac{7}{7}$

Step 3.3

Divide $7$ by $7$ .

$1$