Precalculus Examples

$f (x) = 6 x - 3$ , $(6, 9)$

Substitute using the average rate of change formula.

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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.

$\frac{f (9) - f (6)}{(9) - (6)}$

Substitute the equation $y = 6 x - 3$ for $f (9)$ and $f (6)$ , replacing $x$ in the function with the corresponding $x$ value.

$\frac{(6 (9) - 3) - (6 (6) - 3)}{(9) - (6)}$

Simplify the expression.

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Simplify the numerator.

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Multiply $6$ by $9$ .

$\frac{54 - 3 - (6 (6) - 3)}{(9) - (6)}$

Multiply $6$ by $6$ .

$\frac{54 - 3 - (36 - 3)}{(9) - (6)}$

Subtract $3$ from $36$ .

$\frac{54 - 3 - 1 \cdot 33}{(9) - (6)}$

Multiply $- 1$ by $33$ .

$\frac{54 - 3 - 33}{(9) - (6)}$

Subtract $3$ from $54$ .

$\frac{51 - 33}{(9) - (6)}$

Subtract $33$ from $51$ .

$\frac{18}{(9) - (6)}$

Simplify the denominator.

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Multiply $- 1$ by $6$ .

$\frac{18}{9 - 6}$

Subtract $6$ from $9$ .

$\frac{18}{3}$

Divide $18$ by $3$ .

$6$

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