Algebra Examples

$(\frac{5}{2}, - 1)$ , $(\frac{1}{2}, 9)$

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.

$m = \frac{9 - (- 1)}{\frac{1}{2} - (\frac{5}{2})}$

Step 4

Simplify.

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Step 4.1

Multiply the numerator and denominator of the fraction by $2$ .

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Step 4.1.1

Multiply $\frac{9 - (- 1)}{\frac{1}{2} - \frac{5}{2}}$ by $\frac{2}{2}$ .

$m = \frac{2}{2} \cdot \frac{9 - (- 1)}{\frac{1}{2} - \frac{5}{2}}$

Step 4.1.2

Combine.

$m = \frac{2 (9 - (- 1))}{2 (\frac{1}{2} - \frac{5}{2})}$

Step 4.2

Apply the distributive property.

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

Step 4.3

Simplify by cancelling.

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Step 4.3.1

Cancel the common factor of $2$ .

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Step 4.3.1.1

Cancel the common factor.

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

Step 4.3.1.2

Rewrite the expression.

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

Step 4.3.2

Cancel the common factor of $2$ .

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Step 4.3.2.1

Move the leading negative in $- \frac{5}{2}$ into the numerator.

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

Step 4.3.2.2

Cancel the common factor.

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

Step 4.3.2.3

Rewrite the expression.

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

Step 4.4

Simplify the numerator.

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Step 4.4.1

Multiply $2$ by $9$ .

$m = \frac{18 + 2 (- (- 1))}{1 - 5}$

Step 4.4.2

Multiply $2 (- (- 1))$ .

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Step 4.4.2.1

Multiply $- 1$ by $- 1$ .

$m = \frac{18 + 2 \cdot 1}{1 - 5}$

Step 4.4.2.2

Multiply $2$ by $1$ .

$m = \frac{18 + 2}{1 - 5}$

Step 4.4.3

Add $18$ and $2$ .

$m = \frac{20}{1 - 5}$

Step 4.5

Simplify the expression.

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Step 4.5.1

Subtract $5$ from $1$ .

$m = \frac{20}{- 4}$

Step 4.5.2

Divide $20$ by $- 4$ .

$m = - 5$

Step 5