Algebra Examples

y = 3 x - 2

$y = 3 x - 2$ ,

(0, 4)

$(0, 4)$

Step 1

Substitute using the average rate of change formula.

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Step 1.1

The average rate of change of a function can be found by calculating the change in

y

$y$ values of the two points divided by the change in

x

$x$ values of the two points.

\frac{f (4) - f (0)}{(4) - (0)}

$\frac{f (4) - f (0)}{(4) - (0)}$

Step 1.2

Substitute the equation

y = 3 x - 2

$y = 3 x - 2$ for

f (4)

$f (4)$ and

f (0)

$f (0)$ , replacing

x

$x$ in the function with the corresponding

x

$x$ value.

\frac{(3 (4) - 2) - (3 (0) - 2)}{(4) - (0)}

$\frac{(3 (4) - 2) - (3 (0) - 2)}{(4) - (0)}$

\frac{(3 (4) - 2) - (3 (0) - 2)}{(4) - (0)}

$\frac{(3 (4) - 2) - (3 (0) - 2)}{(4) - (0)}$

Step 2

Simplify the expression.

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Step 2.1

Simplify the numerator.

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Step 2.1.1

Multiply

3

$3$ by

4

$4$ .

\frac{12 - 2 - (3 (0) - 2)}{4 - (0)}

$\frac{12 - 2 - (3 (0) - 2)}{4 - (0)}$

Step 2.1.2

Multiply

3

$3$ by

0

$0$ .

\frac{12 - 2 - (0 - 2)}{4 - (0)}

$\frac{12 - 2 - (0 - 2)}{4 - (0)}$

Step 2.1.3

Subtract

2

$2$ from

0

$0$ .

\frac{12 - 2 - - 2}{4 - (0)}

$\frac{12 - 2 - - 2}{4 - (0)}$

Step 2.1.4

Multiply

- 1

$- 1$ by

- 2

$- 2$ .

\frac{12 - 2 + 2}{4 - (0)}

$\frac{12 - 2 + 2}{4 - (0)}$

Step 2.1.5

Subtract

2

$2$ from

12

$12$ .

\frac{10 + 2}{4 - (0)}

$\frac{10 + 2}{4 - (0)}$

Step 2.1.6

Add

10

$10$ and

2

$2$ .

\frac{12}{4 - (0)}

$\frac{12}{4 - (0)}$

\frac{12}{4 - (0)}

$\frac{12}{4 - (0)}$

Step 2.2

Simplify the denominator.

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Step 2.2.1

Multiply

- 1

$- 1$ by

0

$0$ .

\frac{12}{4 + 0}

$\frac{12}{4 + 0}$

Step 2.2.2

Add

4

$4$ and

0

$0$ .

\frac{12}{4}

$\frac{12}{4}$

\frac{12}{4}

$\frac{12}{4}$

Step 2.3

Divide

12

$12$ by

4

$4$ .

3

$3$

3

$3$

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