Precalculus Examples

$(- 4, 10)$ and $(8, - 2)$

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.

$m = \frac{- 2 - (10)}{8 - (- 4)}$

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 $- 2 - (10)$ and $8 - (- 4)$ .

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Step 4.1.1.1

Rewrite $- 2$ as $- 1 (2)$ .

$m = \frac{- 1 \cdot 2 - (10)}{8 - (- 4)}$

Step 4.1.1.2

Factor $- 1$ out of $- 1 (2) - (10)$ .

$m = \frac{- 1 (2 + 10)}{8 - (- 4)}$

Step 4.1.1.3

Reorder terms.

$m = \frac{- 1 (2 + 10)}{8 - 4 \cdot - 1}$

Step 4.1.1.4

Factor $2$ out of $- 1 (2 + 10)$ .

$m = \frac{2 (- 1 (1 + 5))}{8 - 4 \cdot - 1}$

Step 4.1.1.5

Cancel the common factors.

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Step 4.1.1.5.1

Factor $2$ out of $8$ .

$m = \frac{2 (- 1 (1 + 5))}{2 (4) - 4 \cdot - 1}$

Step 4.1.1.5.2

Factor $2$ out of $- 4 \cdot - 1$ .

$m = \frac{2 (- 1 (1 + 5))}{2 (4) + 2 (- 2 \cdot - 1)}$

Step 4.1.1.5.3

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

$m = \frac{2 (- 1 (1 + 5))}{2 (4 - 2 \cdot - 1)}$

Step 4.1.1.5.4

Cancel the common factor.

$m = \frac{2 (- 1 (1 + 5))}{2 (4 - 2 \cdot - 1)}$

Step 4.1.1.5.5

Rewrite the expression.

$m = \frac{- 1 (1 + 5)}{4 - 2 \cdot - 1}$

Step 4.1.2

Add $1$ and $5$ .

$m = \frac{- 1 \cdot 6}{4 - 2 \cdot - 1}$

Step 4.2

Simplify the denominator.

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Step 4.2.1

Multiply $- 2$ by $- 1$ .

$m = \frac{- 1 \cdot 6}{4 + 2}$

Step 4.2.2

Add $4$ and $2$ .

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

Step 4.3

Simplify the expression.

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Step 4.3.1

Multiply $- 1$ by $6$ .

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

Step 4.3.2

Divide $- 6$ by $6$ .

$m = - 1$

Step 5