Find the Average Rate of Change

$y - 2 = 3 x$ , $(0, 2)$ , $(2, 8)$

Step 1

Write $y = 3 x + 2$ as a function.

$f (x) = 3 x + 2$

Step 2

Add $2$ to both sides of the equation.

$y = 3 x + 2$

Step 3

Substitute using the average rate of change formula.

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Step 3.1

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.

$\frac{f (2) - f (0)}{(2) - (0)}$

Step 3.2

Substitute the equation $y = 3 x + 2$ for $f (2)$ and $f (0)$ , replacing $x$ in the function with the corresponding $x$ value.

$\frac{(3 (2) + 2) - (3 (0) + 2)}{(2) - (0)}$

Step 4

Simplify the expression.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Multiply $3$ by $2$ .

$\frac{6 + 2 - (3 (0) + 2)}{2 - (0)}$

Step 4.1.2

Multiply $3$ by $0$ .

$\frac{6 + 2 - (0 + 2)}{2 - (0)}$

Step 4.1.3

Add $0$ and $2$ .

$\frac{6 + 2 - 1 \cdot 2}{2 - (0)}$

Step 4.1.4

Multiply $- 1$ by $2$ .

$\frac{6 + 2 - 2}{2 - (0)}$

Step 4.1.5

Add $6$ and $2$ .

$\frac{8 - 2}{2 - (0)}$

Step 4.1.6

Subtract $2$ from $8$ .

$\frac{6}{2 - (0)}$

Step 4.2

Simplify the denominator.

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Step 4.2.1

Multiply $- 1$ by $0$ .

$\frac{6}{2 + 0}$

Step 4.2.2

Add $2$ and $0$ .

$\frac{6}{2}$

Step 4.3

Divide $6$ by $2$ .

$3$

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