Precalculus Examples

$(- 8, - 1)$ and $(- 12, - 2)$

Step 1

Slope is equal to the change in $y$ over the change in $x$ , or rise over run.

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

Step 2

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

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

Step 3

Substitute in the values of $x$ and $y$ into the equation to find the slope.

$m = \frac{- 2 - (- 1)}{- 12 - (- 8)}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Multiply $- 1$ by $- 1$ .

$m = \frac{- 2 + 1}{- 12 - (- 8)}$

Step 4.1.2

Add $- 2$ and $1$ .

$m = \frac{- 1}{- 12 - (- 8)}$

Step 4.2

Simplify the denominator.

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Step 4.2.1

Multiply $- 1$ by $- 8$ .

$m = \frac{- 1}{- 12 + 8}$

Step 4.2.2

Add $- 12$ and $8$ .

$m = \frac{- 1}{- 4}$

Step 4.3

Dividing two negative values results in a positive value.

$m = \frac{1}{4}$

Step 5