Finite Math Examples

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

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.

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

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 $\frac{\frac{3}{2} - - \frac{1}{2}}{5 - (2)}$ by $\frac{2}{2}$ .

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

Step 4.1.2

Combine.

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

Step 4.2

Apply the distributive property.

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

Step 4.3

Cancel the common factor of $2$ .

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Step 4.3.1

Cancel the common factor.

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

Step 4.3.2

Rewrite the expression.

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

Step 4.4

Simplify the numerator.

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Step 4.4.1

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

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Step 4.4.1.1

Multiply $- 1$ by $- 1$ .

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

Step 4.4.1.2

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

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

Step 4.4.2

Cancel the common factor of $2$ .

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Step 4.4.2.1

Cancel the common factor.

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

Step 4.4.2.2

Rewrite the expression.

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

Step 4.4.3

Add $3$ and $1$ .

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

Step 4.5

Simplify the denominator.

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Step 4.5.1

Multiply $2$ by $5$ .

$m = \frac{4}{10 + 2 (- (2))}$

Step 4.5.2

Multiply $2 (- (2))$ .

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Step 4.5.2.1

Multiply $- 1$ by $2$ .

$m = \frac{4}{10 + 2 \cdot - 2}$

Step 4.5.2.2

Multiply $2$ by $- 2$ .

$m = \frac{4}{10 - 4}$

Step 4.5.3

Subtract $4$ from $10$ .

$m = \frac{4}{6}$

Step 4.6

Cancel the common factor of $4$ and $6$ .

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Step 4.6.1

Factor $2$ out of $4$ .

$m = \frac{2 (2)}{6}$

Step 4.6.2

Cancel the common factors.

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Step 4.6.2.1

Factor $2$ out of $6$ .

$m = \frac{2 \cdot 2}{2 \cdot 3}$

Step 4.6.2.2

Cancel the common factor.

$m = \frac{2 \cdot 2}{2 \cdot 3}$

Step 4.6.2.3

Rewrite the expression.

$m = \frac{2}{3}$

Step 5