Precalculus Examples

$(- 8, - 6)$ and $(- 18, 6)$

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.

$m = \frac{6 - (- 6)}{- 18 - (- 8)}$

Step 4

Simplify.

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Step 4.1

Reduce the expression by cancelling the common factors.

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Step 4.1.1

Cancel the common factor of $6 - (- 6)$ and $- 18 - (- 8)$ .

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Step 4.1.1.1

Rewrite $6$ as $- 1 (- 6)$ .

$m = \frac{- 1 \cdot - 6 - (- 6)}{- 18 - (- 8)}$

Step 4.1.1.2

Factor $- 1$ out of $- 1 (- 6) - (- 6)$ .

$m = \frac{- 1 (- 6 - 6)}{- 18 - (- 8)}$

Step 4.1.1.3

Reorder terms.

$m = \frac{- 1 (- 6 - 6)}{- 18 - 8 \cdot - 1}$

Step 4.1.1.4

Factor $2$ out of $- 1 (- 6 - 6)$ .

$m = \frac{2 (- 1 (- 3 - 3))}{- 18 - 8 \cdot - 1}$

Step 4.1.1.5

Cancel the common factors.

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Step 4.1.1.5.1

Factor $2$ out of $- 18$ .

$m = \frac{2 (- 1 (- 3 - 3))}{2 (- 9) - 8 \cdot - 1}$

Step 4.1.1.5.2

Factor $2$ out of $- 8 \cdot - 1$ .

$m = \frac{2 (- 1 (- 3 - 3))}{2 (- 9) + 2 (- 4 \cdot - 1)}$

Step 4.1.1.5.3

Factor $2$ out of $2 (- 9) + 2 (- 4 \cdot - 1)$ .

$m = \frac{2 (- 1 (- 3 - 3))}{2 (- 9 - 4 \cdot - 1)}$

Step 4.1.1.5.4

Cancel the common factor.

$m = \frac{2 (- 1 (- 3 - 3))}{2 (- 9 - 4 \cdot - 1)}$

Step 4.1.1.5.5

Rewrite the expression.

$m = \frac{- 1 (- 3 - 3)}{- 9 - 4 \cdot - 1}$

Step 4.1.2

Subtract $3$ from $- 3$ .

$m = \frac{- 1 \cdot - 6}{- 9 - 4 \cdot - 1}$

Step 4.2

Simplify the denominator.

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Step 4.2.1

Multiply $- 4$ by $- 1$ .

$m = \frac{- 1 \cdot - 6}{- 9 + 4}$

Step 4.2.2

Add $- 9$ and $4$ .

$m = \frac{- 1 \cdot - 6}{- 5}$

Step 4.3

Simplify the expression.

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Step 4.3.1

Multiply $- 1$ by $- 6$ .

$m = \frac{6}{- 5}$

Step 4.3.2

Move the negative in front of the fraction.

$m = - \frac{6}{5}$

Step 5