Algebra Examples

$f (x) = 6 x - 3$ , $(1, 4)$

Step 1

Write $f (x) = 6 x - 3$ as an equation.

$y = 6 x - 3$

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.

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

Step 2.2

Substitute the equation $y = 6 x - 3$ for $f (4)$ and $f (1)$ , replacing $x$ in the function with the corresponding $x$ value.

$\frac{(6 (4) - 3) - (6 (1) - 3)}{(4) - (1)}$

Step 3

Simplify the expression.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Multiply $6$ by $4$ .

$\frac{24 - 3 - (6 (1) - 3)}{4 - (1)}$

Step 3.1.2

Multiply $6$ by $1$ .

$\frac{24 - 3 - (6 - 3)}{4 - (1)}$

Step 3.1.3

Subtract $3$ from $6$ .

$\frac{24 - 3 - 1 \cdot 3}{4 - (1)}$

Step 3.1.4

Multiply $- 1$ by $3$ .

$\frac{24 - 3 - 3}{4 - (1)}$

Step 3.1.5

Subtract $3$ from $24$ .

$\frac{21 - 3}{4 - (1)}$

Step 3.1.6

Subtract $3$ from $21$ .

$\frac{18}{4 - (1)}$

Step 3.2

Simplify the denominator.

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Step 3.2.1

Multiply $- 1$ by $1$ .

$\frac{18}{4 - 1}$

Step 3.2.2

Subtract $1$ from $4$ .

$\frac{18}{3}$

Step 3.3

Divide $18$ by $3$ .

$6$

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