Precalculus Examples

$(- 28, \frac{46}{9})$ , $(0, - \frac{10}{9})$

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.

$m = \frac{- \frac{10}{9} - (\frac{46}{9})}{0 - (- 28)}$

Step 4

Simplify.

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Step 4.1

Multiply the numerator and denominator of the fraction by $9$ .

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Step 4.1.1

Multiply $\frac{- \frac{10}{9} - \frac{46}{9}}{0 - (- 28)}$ by $\frac{9}{9}$ .

$m = \frac{9}{9} \cdot \frac{- \frac{10}{9} - \frac{46}{9}}{0 - (- 28)}$

Step 4.1.2

Combine.

$m = \frac{9 (- \frac{10}{9} - \frac{46}{9})}{9 (0 - (- 28))}$

Step 4.2

Apply the distributive property.

$m = \frac{9 (- \frac{10}{9}) + 9 (- \frac{46}{9})}{9 \cdot 0 + 9 (- (- 28))}$

Step 4.3

Simplify by cancelling.

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Step 4.3.1

Cancel the common factor of $9$ .

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Step 4.3.1.1

Move the leading negative in $- \frac{10}{9}$ into the numerator.

$m = \frac{9 (\frac{- 10}{9}) + 9 (- \frac{46}{9})}{9 \cdot 0 + 9 (- (- 28))}$

Step 4.3.1.2

Cancel the common factor.

$m = \frac{9 (\frac{- 10}{9}) + 9 (- \frac{46}{9})}{9 \cdot 0 + 9 (- (- 28))}$

Step 4.3.1.3

Rewrite the expression.

$m = \frac{- 10 + 9 (- \frac{46}{9})}{9 \cdot 0 + 9 (- (- 28))}$

Step 4.3.2

Cancel the common factor of $9$ .

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Step 4.3.2.1

Move the leading negative in $- \frac{46}{9}$ into the numerator.

$m = \frac{- 10 + 9 (\frac{- 46}{9})}{9 \cdot 0 + 9 (- (- 28))}$

Step 4.3.2.2

Cancel the common factor.

$m = \frac{- 10 + 9 (\frac{- 46}{9})}{9 \cdot 0 + 9 (- (- 28))}$

Step 4.3.2.3

Rewrite the expression.

$m = \frac{- 10 - 46}{9 \cdot 0 + 9 (- (- 28))}$

Step 4.4

Reduce the expression by cancelling the common factors.

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Step 4.4.1

Cancel the common factor of $- 10 - 46$ and $9 \cdot 0 + 9 (- (- 28))$ .

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Step 4.4.1.1

Reorder terms.

$m = \frac{- 10 - 46}{- 28 \cdot - 1 \cdot 9 + 0 \cdot 9}$

Step 4.4.1.2

Factor $2$ out of $- 10$ .

$m = \frac{2 (- 5) - 46}{- 28 \cdot - 1 \cdot 9 + 0 \cdot 9}$

Step 4.4.1.3

Factor $2$ out of $- 46$ .

$m = \frac{2 \cdot - 5 + 2 \cdot - 23}{- 28 \cdot - 1 \cdot 9 + 0 \cdot 9}$

Step 4.4.1.4

Factor $2$ out of $2 \cdot - 5 + 2 \cdot - 23$ .

$m = \frac{2 \cdot (- 5 - 23)}{- 28 \cdot - 1 \cdot 9 + 0 \cdot 9}$

Step 4.4.1.5

Cancel the common factors.

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Step 4.4.1.5.1

Factor $2$ out of $- 28 \cdot - 1 \cdot 9$ .

$m = \frac{2 \cdot (- 5 - 23)}{2 (- 14 \cdot - 1 \cdot 9) + 0 \cdot 9}$

Step 4.4.1.5.2

Factor $2$ out of $0 \cdot 9$ .

$m = \frac{2 \cdot (- 5 - 23)}{2 (- 14 \cdot - 1 \cdot 9) + 2 (0 \cdot 9)}$

Step 4.4.1.5.3

Factor $2$ out of $2 (- 14 \cdot - 1 \cdot 9) + 2 (0 \cdot 9)$ .

$m = \frac{2 \cdot (- 5 - 23)}{2 (- 14 \cdot - 1 \cdot 9 + 0 \cdot 9)}$

Step 4.4.1.5.4

Cancel the common factor.

$m = \frac{2 \cdot (- 5 - 23)}{2 (- 14 \cdot - 1 \cdot 9 + 0 \cdot 9)}$

Step 4.4.1.5.5

Rewrite the expression.

$m = \frac{- 5 - 23}{- 14 \cdot - 1 \cdot 9 + 0 \cdot 9}$

Step 4.4.2

Subtract $23$ from $- 5$ .

$m = \frac{- 28}{- 14 \cdot - 1 \cdot 9 + 0 \cdot 9}$

Step 4.5

Simplify the denominator.

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Step 4.5.1

Multiply $- 14 \cdot - 1 \cdot 9$ .

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Step 4.5.1.1

Multiply $- 14$ by $- 1$ .

$m = \frac{- 28}{14 \cdot 9 + 0 \cdot 9}$

Step 4.5.1.2

Multiply $14$ by $9$ .

$m = \frac{- 28}{126 + 0 \cdot 9}$

Step 4.5.2

Multiply $0$ by $9$ .

$m = \frac{- 28}{126 + 0}$

Step 4.5.3

Add $126$ and $0$ .

$m = \frac{- 28}{126}$

Step 4.6

Reduce the expression by cancelling the common factors.

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Step 4.6.1

Cancel the common factor of $- 28$ and $126$ .

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Step 4.6.1.1

Factor $14$ out of $- 28$ .

$m = \frac{14 (- 2)}{126}$

Step 4.6.1.2

Cancel the common factors.

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Step 4.6.1.2.1

Factor $14$ out of $126$ .

$m = \frac{14 \cdot - 2}{14 \cdot 9}$

Step 4.6.1.2.2

Cancel the common factor.

$m = \frac{14 \cdot - 2}{14 \cdot 9}$

Step 4.6.1.2.3

Rewrite the expression.

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

Step 4.6.2

Move the negative in front of the fraction.

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

Step 5