Algebra Examples

y = 2 x - 2

$y = 2 x - 2$ ,

[- 2, 7]

$[- 2, 7]$

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 (7) - f (- 2)}{(7) - (- 2)}

$\frac{f (7) - f (- 2)}{(7) - (- 2)}$

Step 1.2

Substitute the equation

y = 2 x - 2

$y = 2 x - 2$ for

f (7)

$f (7)$ and

f (- 2)

$f (- 2)$ , replacing

x

$x$ in the function with the corresponding

x

$x$ value.

\frac{(2 (7) - 2) - (2 (- 2) - 2)}{(7) - (- 2)}

$\frac{(2 (7) - 2) - (2 (- 2) - 2)}{(7) - (- 2)}$

\frac{(2 (7) - 2) - (2 (- 2) - 2)}{(7) - (- 2)}

$\frac{(2 (7) - 2) - (2 (- 2) - 2)}{(7) - (- 2)}$

Step 2

Simplify the expression.

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Step 2.1

Simplify the numerator.

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Step 2.1.1

Multiply

2

$2$ by

7

$7$ .

\frac{14 - 2 - (2 (- 2) - 2)}{7 - (- 2)}

$\frac{14 - 2 - (2 (- 2) - 2)}{7 - (- 2)}$

Step 2.1.2

Multiply

2

$2$ by

- 2

$- 2$ .

\frac{14 - 2 - (- 4 - 2)}{7 - (- 2)}

$\frac{14 - 2 - (- 4 - 2)}{7 - (- 2)}$

Step 2.1.3

Subtract

2

$2$ from

- 4

$- 4$ .

\frac{14 - 2 - - 6}{7 - (- 2)}

$\frac{14 - 2 - - 6}{7 - (- 2)}$

Step 2.1.4

Multiply

- 1

$- 1$ by

- 6

$- 6$ .

\frac{14 - 2 + 6}{7 - (- 2)}

$\frac{14 - 2 + 6}{7 - (- 2)}$

Step 2.1.5

Subtract

2

$2$ from

14

$14$ .

\frac{12 + 6}{7 - (- 2)}

$\frac{12 + 6}{7 - (- 2)}$

Step 2.1.6

Add

12

$12$ and

6

$6$ .

\frac{18}{7 - (- 2)}

$\frac{18}{7 - (- 2)}$

\frac{18}{7 - (- 2)}

$\frac{18}{7 - (- 2)}$

Step 2.2

Simplify the denominator.

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Step 2.2.1

Multiply

- 1

$- 1$ by

- 2

$- 2$ .

\frac{18}{7 + 2}

$\frac{18}{7 + 2}$

Step 2.2.2

Add

7

$7$ and

2

$2$ .

\frac{18}{9}

$\frac{18}{9}$

\frac{18}{9}

$\frac{18}{9}$

Step 2.3

Divide

18

$18$ by

9

$9$ .

2

$2$

2

$2$

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