Precalculus Examples

Find the slope of the line passing through the points $(- 7, 8)$ and $(5, - 7)$

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.

$m = \frac{- 7 - (8)}{5 - (- 7)}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Multiply $- 1$ by $8$ .

$m = \frac{- 7 - 8}{5 - (- 7)}$

Step 4.1.2

Subtract $8$ from $- 7$ .

$m = \frac{- 15}{5 - (- 7)}$

Step 4.2

Simplify the denominator.

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Step 4.2.1

Multiply $- 1$ by $- 7$ .

$m = \frac{- 15}{5 + 7}$

Step 4.2.2

Add $5$ and $7$ .

$m = \frac{- 15}{12}$

Step 4.3

Reduce the expression by cancelling the common factors.

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Step 4.3.1

Cancel the common factor of $- 15$ and $12$ .

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Step 4.3.1.1

Factor $3$ out of $- 15$ .

$m = \frac{3 (- 5)}{12}$

Step 4.3.1.2

Cancel the common factors.

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Step 4.3.1.2.1

Factor $3$ out of $12$ .

$m = \frac{3 \cdot - 5}{3 \cdot 4}$

Step 4.3.1.2.2

Cancel the common factor.

$m = \frac{3 \cdot - 5}{3 \cdot 4}$

Step 4.3.1.2.3

Rewrite the expression.

$m = \frac{- 5}{4}$

Step 4.3.2

Move the negative in front of the fraction.

$m = - \frac{5}{4}$

Step 5