Finite Math Examples

$f (x) = 9 x - 4$ , $(5, 9)$

Step 1

Write $f (x) = 9 x - 4$ as an equation.

$y = 9 x - 4$

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.

$\frac{f (9) - f (5)}{(9) - (5)}$

Step 2.2

Substitute the equation $y = 9 x - 4$ for $f (9)$ and $f (5)$ , replacing $x$ in the function with the corresponding $x$ value.

$\frac{(9 (9) - 4) - (9 (5) - 4)}{(9) - (5)}$

Step 3

Simplify the expression.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Multiply $9$ by $9$ .

$\frac{81 - 4 - (9 (5) - 4)}{9 - (5)}$

Step 3.1.2

Multiply $9$ by $5$ .

$\frac{81 - 4 - (45 - 4)}{9 - (5)}$

Step 3.1.3

Subtract $4$ from $45$ .

$\frac{81 - 4 - 1 \cdot 41}{9 - (5)}$

Step 3.1.4

Multiply $- 1$ by $41$ .

$\frac{81 - 4 - 41}{9 - (5)}$

Step 3.1.5

Subtract $4$ from $81$ .

$\frac{77 - 41}{9 - (5)}$

Step 3.1.6

Subtract $41$ from $77$ .

$\frac{36}{9 - (5)}$

Step 3.2

Simplify the denominator.

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Step 3.2.1

Multiply $- 1$ by $5$ .

$\frac{36}{9 - 5}$

Step 3.2.2

Subtract $5$ from $9$ .

$\frac{36}{4}$

Step 3.3

Divide $36$ by $4$ .

$9$