Precalculus Examples

$(\frac{3}{5}, \frac{2}{3})$ and $(- \frac{4}{5}, \frac{1}{3})$

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.

$m = \frac{\frac{1}{3} - (\frac{2}{3})}{- \frac{4}{5} - (\frac{3}{5})}$

Step 4

Simplify.

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Step 4.1

Multiply the numerator and denominator of the fraction by $15$ .

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Step 4.1.1

Multiply $\frac{\frac{1}{3} - \frac{2}{3}}{- \frac{4}{5} - \frac{3}{5}}$ by $\frac{15}{15}$ .

$m = \frac{15}{15} \cdot \frac{\frac{1}{3} - \frac{2}{3}}{- \frac{4}{5} - \frac{3}{5}}$

Step 4.1.2

Combine.

$m = \frac{15 (\frac{1}{3} - \frac{2}{3})}{15 (- \frac{4}{5} - \frac{3}{5})}$

Step 4.2

Apply the distributive property.

$m = \frac{15 (\frac{1}{3}) + 15 (- \frac{2}{3})}{15 (- \frac{4}{5}) + 15 (- \frac{3}{5})}$

Step 4.3

Simplify by cancelling.

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Step 4.3.1

Cancel the common factor of $3$ .

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Step 4.3.1.1

Factor $3$ out of $15$ .

$m = \frac{3 (5) (\frac{1}{3}) + 15 (- \frac{2}{3})}{15 (- \frac{4}{5}) + 15 (- \frac{3}{5})}$

Step 4.3.1.2

Cancel the common factor.

$m = \frac{3 \cdot (5 (\frac{1}{3})) + 15 (- \frac{2}{3})}{15 (- \frac{4}{5}) + 15 (- \frac{3}{5})}$

Step 4.3.1.3

Rewrite the expression.

$m = \frac{5 + 15 (- \frac{2}{3})}{15 (- \frac{4}{5}) + 15 (- \frac{3}{5})}$

Step 4.3.2

Cancel the common factor of $3$ .

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Step 4.3.2.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$m = \frac{5 + 15 (\frac{- 2}{3})}{15 (- \frac{4}{5}) + 15 (- \frac{3}{5})}$

Step 4.3.2.2

Factor $3$ out of $15$ .

$m = \frac{5 + 3 (5) (\frac{- 2}{3})}{15 (- \frac{4}{5}) + 15 (- \frac{3}{5})}$

Step 4.3.2.3

Cancel the common factor.

$m = \frac{5 + 3 \cdot (5 (\frac{- 2}{3}))}{15 (- \frac{4}{5}) + 15 (- \frac{3}{5})}$

Step 4.3.2.4

Rewrite the expression.

$m = \frac{5 + 5 \cdot - 2}{15 (- \frac{4}{5}) + 15 (- \frac{3}{5})}$

Step 4.3.3

Multiply $5$ by $- 2$ .

$m = \frac{5 - 10}{15 (- \frac{4}{5}) + 15 (- \frac{3}{5})}$

Step 4.3.4

Cancel the common factor of $5$ .

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Step 4.3.4.1

Move the leading negative in $- \frac{4}{5}$ into the numerator.

$m = \frac{5 - 10}{15 (\frac{- 4}{5}) + 15 (- \frac{3}{5})}$

Step 4.3.4.2

Factor $5$ out of $15$ .

$m = \frac{5 - 10}{5 (3) (\frac{- 4}{5}) + 15 (- \frac{3}{5})}$

Step 4.3.4.3

Cancel the common factor.

$m = \frac{5 - 10}{5 \cdot (3 (\frac{- 4}{5})) + 15 (- \frac{3}{5})}$

Step 4.3.4.4

Rewrite the expression.

$m = \frac{5 - 10}{3 \cdot - 4 + 15 (- \frac{3}{5})}$

Step 4.3.5

Multiply $3$ by $- 4$ .

$m = \frac{5 - 10}{- 12 + 15 (- \frac{3}{5})}$

Step 4.3.6

Cancel the common factor of $5$ .

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Step 4.3.6.1

Move the leading negative in $- \frac{3}{5}$ into the numerator.

$m = \frac{5 - 10}{- 12 + 15 (\frac{- 3}{5})}$

Step 4.3.6.2

Factor $5$ out of $15$ .

$m = \frac{5 - 10}{- 12 + 5 (3) (\frac{- 3}{5})}$

Step 4.3.6.3

Cancel the common factor.

$m = \frac{5 - 10}{- 12 + 5 \cdot (3 (\frac{- 3}{5}))}$

Step 4.3.6.4

Rewrite the expression.

$m = \frac{5 - 10}{- 12 + 3 \cdot - 3}$

Step 4.3.7

Multiply $3$ by $- 3$ .

$m = \frac{5 - 10}{- 12 - 9}$

Step 4.4

Reduce the expression by cancelling the common factors.

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Step 4.4.1

Subtract $10$ from $5$ .

$m = \frac{- 5}{- 12 - 9}$

Step 4.4.2

Subtract $9$ from $- 12$ .

$m = \frac{- 5}{- 21}$

Step 4.4.3

Dividing two negative values results in a positive value.

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

Step 5