Precalculus Examples

$(- \frac{1}{2}, 1)$ , $(- 3, \frac{2}{3})$

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.

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

Step 4

Simplify.

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Step 4.1

Multiply the numerator and denominator of the fraction by $3$ .

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Step 4.1.1

Multiply $\frac{\frac{2}{3} - (1)}{- 3 - - \frac{1}{2}}$ by $\frac{3}{3}$ .

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

Step 4.1.2

Combine.

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

Step 4.2

Apply the distributive property.

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

Step 4.3

Cancel the common factor of $3$ .

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Step 4.3.1

Cancel the common factor.

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

Step 4.3.2

Rewrite the expression.

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

Step 4.4

Simplify the numerator.

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Step 4.4.1

Multiply $3 (- (1))$ .

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Step 4.4.1.1

Multiply $- 1$ by $1$ .

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

Step 4.4.1.2

Multiply $3$ by $- 1$ .

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

Step 4.4.2

Subtract $3$ from $2$ .

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

Step 4.5

Simplify the denominator.

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Step 4.5.1

Multiply $3$ by $- 3$ .

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

Step 4.5.2

Multiply $- - \frac{1}{2}$ .

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Step 4.5.2.1

Multiply $- 1$ by $- 1$ .

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

Step 4.5.2.2

Multiply $\frac{1}{2}$ by $1$ .

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

Step 4.5.3

Combine $3$ and $\frac{1}{2}$ .

$m = \frac{- 1}{- 9 + \frac{3}{2}}$

Step 4.5.4

To write $- 9$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 4.5.5

Combine $- 9$ and $\frac{2}{2}$ .

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

Step 4.5.6

Combine the numerators over the common denominator.

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

Step 4.5.7

Simplify the numerator.

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Step 4.5.7.1

Multiply $- 9$ by $2$ .

$m = \frac{- 1}{\frac{- 18 + 3}{2}}$

Step 4.5.7.2

Add $- 18$ and $3$ .

$m = \frac{- 1}{\frac{- 15}{2}}$

Step 4.5.8

Move the negative in front of the fraction.

$m = \frac{- 1}{- \frac{15}{2}}$

Step 4.6

Dividing two negative values results in a positive value.

$m = \frac{1}{\frac{15}{2}}$

Step 4.7

Multiply the numerator by the reciprocal of the denominator.

$m = 1 (\frac{2}{15})$

Step 4.8

Multiply $\frac{2}{15}$ by $1$ .

$m = \frac{2}{15}$

Step 5