Precalculus Examples

$(3, 8)$ and $(9, 10)$

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.

$m = \frac{10 - (8)}{9 - (3)}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Multiply $- 1$ by $8$ .

$m = \frac{10 - 8}{9 - (3)}$

Step 4.1.2

Subtract $8$ from $10$ .

$m = \frac{2}{9 - (3)}$

Step 4.2

Simplify the denominator.

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Step 4.2.1

Multiply $- 1$ by $3$ .

$m = \frac{2}{9 - 3}$

Step 4.2.2

Subtract $3$ from $9$ .

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

Step 4.3

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

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Step 4.3.1

Factor $2$ out of $2$ .

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

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Factor $2$ out of $6$ .

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

Step 4.3.2.2

Cancel the common factor.

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

Step 4.3.2.3

Rewrite the expression.

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

Step 5