Precalculus Examples

$(\frac{5}{8}, - 2)$ and $(- \frac{1}{4}, - \frac{1}{4})$

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.

$m = \frac{- \frac{1}{4} - (- 2)}{- \frac{1}{4} - (\frac{5}{8})}$

Step 4

Simplify.

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Step 4.1

Multiply the numerator and denominator of the fraction by $8$ .

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Step 4.1.1

Multiply $\frac{- \frac{1}{4} - (- 2)}{- \frac{1}{4} - \frac{5}{8}}$ by $\frac{8}{8}$ .

$m = \frac{8}{8} \cdot \frac{- \frac{1}{4} - (- 2)}{- \frac{1}{4} - \frac{5}{8}}$

Step 4.1.2

Combine.

$m = \frac{8 (- \frac{1}{4} - (- 2))}{8 (- \frac{1}{4} - \frac{5}{8})}$

Step 4.2

Apply the distributive property.

$m = \frac{8 (- \frac{1}{4}) + 8 (- (- 2))}{8 (- \frac{1}{4}) + 8 (- \frac{5}{8})}$

Step 4.3

Simplify by cancelling.

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Step 4.3.1

Cancel the common factor of $4$ .

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Step 4.3.1.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$m = \frac{8 (\frac{- 1}{4}) + 8 (- (- 2))}{8 (- \frac{1}{4}) + 8 (- \frac{5}{8})}$

Step 4.3.1.2

Factor $4$ out of $8$ .

$m = \frac{4 (2) (\frac{- 1}{4}) + 8 (- (- 2))}{8 (- \frac{1}{4}) + 8 (- \frac{5}{8})}$

Step 4.3.1.3

Cancel the common factor.

$m = \frac{4 \cdot (2 (\frac{- 1}{4})) + 8 (- (- 2))}{8 (- \frac{1}{4}) + 8 (- \frac{5}{8})}$

Step 4.3.1.4

Rewrite the expression.

$m = \frac{2 \cdot - 1 + 8 (- (- 2))}{8 (- \frac{1}{4}) + 8 (- \frac{5}{8})}$

Step 4.3.2

Multiply $2$ by $- 1$ .

$m = \frac{- 2 + 8 (- (- 2))}{8 (- \frac{1}{4}) + 8 (- \frac{5}{8})}$

Step 4.3.3

Cancel the common factor of $4$ .

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Step 4.3.3.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$m = \frac{- 2 + 8 (- (- 2))}{8 (\frac{- 1}{4}) + 8 (- \frac{5}{8})}$

Step 4.3.3.2

Factor $4$ out of $8$ .

$m = \frac{- 2 + 8 (- (- 2))}{4 (2) (\frac{- 1}{4}) + 8 (- \frac{5}{8})}$

Step 4.3.3.3

Cancel the common factor.

$m = \frac{- 2 + 8 (- (- 2))}{4 \cdot (2 (\frac{- 1}{4})) + 8 (- \frac{5}{8})}$

Step 4.3.3.4

Rewrite the expression.

$m = \frac{- 2 + 8 (- (- 2))}{2 \cdot - 1 + 8 (- \frac{5}{8})}$

Step 4.3.4

Multiply $2$ by $- 1$ .

$m = \frac{- 2 + 8 (- (- 2))}{- 2 + 8 (- \frac{5}{8})}$

Step 4.3.5

Cancel the common factor of $8$ .

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Step 4.3.5.1

Move the leading negative in $- \frac{5}{8}$ into the numerator.

$m = \frac{- 2 + 8 (- (- 2))}{- 2 + 8 (\frac{- 5}{8})}$

Step 4.3.5.2

Cancel the common factor.

$m = \frac{- 2 + 8 (- (- 2))}{- 2 + 8 (\frac{- 5}{8})}$

Step 4.3.5.3

Rewrite the expression.

$m = \frac{- 2 + 8 (- (- 2))}{- 2 - 5}$

Step 4.4

Simplify the numerator.

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Step 4.4.1

Multiply $8 (- (- 2))$ .

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Step 4.4.1.1

Multiply $- 1$ by $- 2$ .

$m = \frac{- 2 + 8 \cdot 2}{- 2 - 5}$

Step 4.4.1.2

Multiply $8$ by $2$ .

$m = \frac{- 2 + 16}{- 2 - 5}$

Step 4.4.2

Add $- 2$ and $16$ .

$m = \frac{14}{- 2 - 5}$

Step 4.5

Simplify the expression.

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Step 4.5.1

Subtract $5$ from $- 2$ .

$m = \frac{14}{- 7}$

Step 4.5.2

Divide $14$ by $- 7$ .

$m = - 2$

Step 5