Precalculus Examples

$(10, - 6)$ and $(8, - 16)$

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.

$m = \frac{- 16 - (- 6)}{8 - (10)}$

Step 4

Simplify.

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Step 4.1

Cancel the common factor of $- 16 - (- 6)$ and $8 - (10)$ .

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Step 4.1.1

Rewrite $8$ as $- 1 (- 8)$ .

$m = \frac{- 16 - (- 6)}{- 1 \cdot - 8 - (10)}$

Step 4.1.2

Factor $- 1$ out of $- 1 (- 8) - (10)$ .

$m = \frac{- 16 - (- 6)}{- 1 (- 8 + 10)}$

Step 4.1.3

Reorder terms.

$m = \frac{- 16 - 6 \cdot - 1}{- 1 (- 8 + 10)}$

Step 4.1.4

Factor $2$ out of $- 16$ .

$m = \frac{2 (- 8) - 6 \cdot - 1}{- 1 (- 8 + 10)}$

Step 4.1.5

Factor $2$ out of $- 6 \cdot - 1$ .

$m = \frac{2 (- 8) + 2 (- 3 \cdot - 1)}{- 1 (- 8 + 10)}$

Step 4.1.6

Factor $2$ out of $2 (- 8) + 2 (- 3 \cdot - 1)$ .

$m = \frac{2 (- 8 - 3 \cdot - 1)}{- 1 (- 8 + 10)}$

Step 4.1.7

Cancel the common factors.

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Step 4.1.7.1

Factor $2$ out of $- 1 (- 8 + 10)$ .

$m = \frac{2 (- 8 - 3 \cdot - 1)}{2 (- 1 (- 4 + 5))}$

Step 4.1.7.2

Cancel the common factor.

$m = \frac{2 (- 8 - 3 \cdot - 1)}{2 (- 1 (- 4 + 5))}$

Step 4.1.7.3

Rewrite the expression.

$m = \frac{- 8 - 3 \cdot - 1}{- 1 (- 4 + 5)}$

Step 4.2

Simplify the numerator.

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Step 4.2.1

Multiply $- 3$ by $- 1$ .

$m = \frac{- 8 + 3}{- 1 (- 4 + 5)}$

Step 4.2.2

Add $- 8$ and $3$ .

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

Step 4.3

Simplify the expression.

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Step 4.3.1

Add $- 4$ and $5$ .

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

Step 4.3.2

Multiply $- 1$ by $1$ .

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

Step 4.3.3

Divide $- 5$ by $- 1$ .

$m = 5$

Step 5