Precalculus Examples

(5, 4)

$(5, 4)$ ,

(- 9, 7)

$(- 9, 7)$

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{7 - (4)}{- 9 - (5)}

$m = \frac{7 - (4)}{- 9 - (5)}$

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{7 - 4}{- 9 - (5)}

$m = \frac{7 - 4}{- 9 - (5)}$

Step 4.1.2

Subtract

4

$4$ from

7

$7$ .

m = \frac{3}{- 9 - (5)}

$m = \frac{3}{- 9 - (5)}$

m = \frac{3}{- 9 - (5)}

$m = \frac{3}{- 9 - (5)}$

Step 4.2

Simplify the denominator.

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Step 4.2.1

Multiply

- 1

$- 1$ by

5

$5$ .

m = \frac{3}{- 9 - 5}

$m = \frac{3}{- 9 - 5}$

Step 4.2.2

Subtract

5

$5$ from

- 9

$- 9$ .

m = \frac{3}{- 14}

$m = \frac{3}{- 14}$

m = \frac{3}{- 14}

$m = \frac{3}{- 14}$

Step 4.3

Move the negative in front of the fraction.

m = - \frac{3}{14}

$m = - \frac{3}{14}$

m = - \frac{3}{14}

$m = - \frac{3}{14}$

Step 5

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