Algebra Examples

f (2) = 4

$f (2) = 4$ ,

g (5) = 3

$g (5) = 3$

Step 1

Slope is equal to the change in

y

$y$ over the change in

x

$x$ , or rise over run.

m = \frac{change in y}{change in x}

$m = \frac{change in y}{change in x}$

Step 2

The change in

x

$x$ is equal to the difference in x-coordinates (also called run), and the change in

y

$y$ is equal to the difference in y-coordinates (also called rise).

m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

Step 3

Substitute in the values of

x

$x$ and

y

$y$ into the equation to find the slope.

m = \frac{3 - (4)}{5 - (2)}

$m = \frac{3 - (4)}{5 - (2)}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Multiply

- 1

$- 1$ by

4

$4$ .

m = \frac{3 - 4}{5 - (2)}

$m = \frac{3 - 4}{5 - (2)}$

Step 4.1.2

Subtract

4

$4$ from

3

$3$ .

m = \frac{- 1}{5 - (2)}

$m = \frac{- 1}{5 - (2)}$

m = \frac{- 1}{5 - (2)}

$m = \frac{- 1}{5 - (2)}$

Step 4.2

Simplify the denominator.

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Step 4.2.1

Multiply

- 1

$- 1$ by

2

$2$ .

m = \frac{- 1}{5 - 2}

$m = \frac{- 1}{5 - 2}$

Step 4.2.2

Subtract

2

$2$ from

5

$5$ .

m = \frac{- 1}{3}

$m = \frac{- 1}{3}$

m = \frac{- 1}{3}

$m = \frac{- 1}{3}$

Step 4.3

Move the negative in front of the fraction.

m = - \frac{1}{3}

$m = - \frac{1}{3}$

m = - \frac{1}{3}

$m = - \frac{1}{3}$

Step 5

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