Precalculus Examples

$(3, - 9)$ and $(- 12, - 6)$

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.

$m = \frac{- 6 - (- 9)}{- 12 - (3)}$

Step 4

Simplify.

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Step 4.1

Cancel the common factor of $- 6 - (- 9)$ and $- 12 - (3)$ .

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Step 4.1.1

Rewrite $- 12$ as $- 1 (12)$ .

$m = \frac{- 6 - (- 9)}{- 1 \cdot 12 - (3)}$

Step 4.1.2

Factor $- 1$ out of $- 1 (12) - (3)$ .

$m = \frac{- 6 - (- 9)}{- 1 (12 + 3)}$

Step 4.1.3

Reorder terms.

$m = \frac{- 6 - 9 \cdot - 1}{- 1 (12 + 3)}$

Step 4.1.4

Factor $3$ out of $- 6$ .

$m = \frac{3 \cdot - 2 - 9 \cdot - 1}{- 1 (12 + 3)}$

Step 4.1.5

Factor $3$ out of $- 9 \cdot - 1$ .

$m = \frac{3 \cdot - 2 + 3 (- 3 \cdot - 1)}{- 1 (12 + 3)}$

Step 4.1.6

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

$m = \frac{3 (- 2 - 3 \cdot - 1)}{- 1 (12 + 3)}$

Step 4.1.7

Cancel the common factors.

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Step 4.1.7.1

Factor $3$ out of $- 1 (12 + 3)$ .

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

Step 4.1.7.2

Cancel the common factor.

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

Step 4.1.7.3

Rewrite the expression.

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

Step 4.2

Simplify the numerator.

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Step 4.2.1

Multiply $- 3$ by $- 1$ .

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

Step 4.2.2

Add $- 2$ and $3$ .

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

Step 4.3

Simplify the expression.

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Step 4.3.1

Add $4$ and $1$ .

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

Step 4.3.2

Multiply $- 1$ by $5$ .

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

Step 4.3.3

Move the negative in front of the fraction.

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

Step 5