Precalculus Examples

$(- 9, 10)$ and $(21, 15)$

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.

$m = \frac{15 - (10)}{21 - (- 9)}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Multiply $- 1$ by $10$ .

$m = \frac{15 - 10}{21 - (- 9)}$

Step 4.1.2

Subtract $10$ from $15$ .

$m = \frac{5}{21 - (- 9)}$

Step 4.2

Simplify the denominator.

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Step 4.2.1

Multiply $- 1$ by $- 9$ .

$m = \frac{5}{21 + 9}$

Step 4.2.2

Add $21$ and $9$ .

$m = \frac{5}{30}$

Step 4.3

Cancel the common factor of $5$ and $30$ .

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Step 4.3.1

Factor $5$ out of $5$ .

$m = \frac{5 (1)}{30}$

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Factor $5$ out of $30$ .

$m = \frac{5 \cdot 1}{5 \cdot 6}$

Step 4.3.2.2

Cancel the common factor.

$m = \frac{5 \cdot 1}{5 \cdot 6}$

Step 4.3.2.3

Rewrite the expression.

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

Step 5