Precalculus Examples

$(5, - 10)$ and $(11, - 12)$

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.

$m = \frac{- 12 - (- 10)}{11 - (5)}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Multiply $- 1$ by $- 10$ .

$m = \frac{- 12 + 10}{11 - (5)}$

Step 4.1.2

Add $- 12$ and $10$ .

$m = \frac{- 2}{11 - (5)}$

Step 4.2

Simplify the denominator.

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Step 4.2.1

Multiply $- 1$ by $5$ .

$m = \frac{- 2}{11 - 5}$

Step 4.2.2

Subtract $5$ from $11$ .

$m = \frac{- 2}{6}$

Step 4.3

Reduce the expression by cancelling the common factors.

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Step 4.3.1

Cancel the common factor of $- 2$ and $6$ .

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Step 4.3.1.1

Factor $2$ out of $- 2$ .

$m = \frac{2 (- 1)}{6}$

Step 4.3.1.2

Cancel the common factors.

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Step 4.3.1.2.1

Factor $2$ out of $6$ .

$m = \frac{2 \cdot - 1}{2 \cdot 3}$

Step 4.3.1.2.2

Cancel the common factor.

$m = \frac{2 \cdot - 1}{2 \cdot 3}$

Step 4.3.1.2.3

Rewrite the expression.

$m = \frac{- 1}{3}$

Step 4.3.2

Move the negative in front of the fraction.

$m = - \frac{1}{3}$

Step 5