Pre-Algebra Examples

$(\frac{1}{6}, - 1)$ , $(\frac{5}{6}, 5)$

Step 1

Find the value of the slope.

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Step 1.1

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 1.2

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 1.3

Substitute in the values of $x$ and $y$ into the equation to find the slope.

$m = \frac{5 - (- 1)}{\frac{5}{6} - (\frac{1}{6})}$

Step 1.4

Simplify.

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Step 1.4.1

Multiply the numerator and denominator of the fraction by $6$ .

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Step 1.4.1.1

Multiply $\frac{5 - (- 1)}{\frac{5}{6} - \frac{1}{6}}$ by $\frac{6}{6}$ .

$m = \frac{6}{6} \cdot \frac{5 - (- 1)}{\frac{5}{6} - \frac{1}{6}}$

Step 1.4.1.2

Combine.

$m = \frac{6 (5 - (- 1))}{6 (\frac{5}{6} - \frac{1}{6})}$

Step 1.4.2

Apply the distributive property.

$m = \frac{6 \cdot 5 + 6 (- (- 1))}{6 (\frac{5}{6}) + 6 (- \frac{1}{6})}$

Step 1.4.3

Simplify by cancelling.

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Step 1.4.3.1

Cancel the common factor of $6$ .

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Step 1.4.3.1.1

Cancel the common factor.

$m = \frac{6 \cdot 5 + 6 (- (- 1))}{6 (\frac{5}{6}) + 6 (- \frac{1}{6})}$

Step 1.4.3.1.2

Rewrite the expression.

$m = \frac{6 \cdot 5 + 6 (- (- 1))}{5 + 6 (- \frac{1}{6})}$

Step 1.4.3.2

Cancel the common factor of $6$ .

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Step 1.4.3.2.1

Move the leading negative in $- \frac{1}{6}$ into the numerator.

$m = \frac{6 \cdot 5 + 6 (- (- 1))}{5 + 6 (\frac{- 1}{6})}$

Step 1.4.3.2.2

Cancel the common factor.

$m = \frac{6 \cdot 5 + 6 (- (- 1))}{5 + 6 (\frac{- 1}{6})}$

Step 1.4.3.2.3

Rewrite the expression.

$m = \frac{6 \cdot 5 + 6 (- (- 1))}{5 - 1}$

Step 1.4.4

Simplify the numerator.

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Step 1.4.4.1

Multiply $6$ by $5$ .

$m = \frac{30 + 6 (- (- 1))}{5 - 1}$

Step 1.4.4.2

Multiply $6 (- (- 1))$ .

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Step 1.4.4.2.1

Multiply $- 1$ by $- 1$ .

$m = \frac{30 + 6 \cdot 1}{5 - 1}$

Step 1.4.4.2.2

Multiply $6$ by $1$ .

$m = \frac{30 + 6}{5 - 1}$

Step 1.4.4.3

Add $30$ and $6$ .

$m = \frac{36}{5 - 1}$

Step 1.4.5

Simplify the expression.

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Step 1.4.5.1

Subtract $1$ from $5$ .

$m = \frac{36}{4}$

Step 1.4.5.2

Divide $36$ by $4$ .

$m = 9$

Step 2

Find the value of the y-intercept.

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Step 2.1

Substitute the value of $m$ into the slope-intercept form of the equation, $y = m x + b$ .

$y = (9) \cdot x + b$

Step 2.2

Substitute the value of $x$ into the slope-intercept form of the equation, $y = m x + b$ .

$y = (9) \cdot (\frac{1}{6}) + b$

Step 2.3

Substitute the value of $y$ into the slope-intercept form of the equation, $y = m x + b$ .

$- 1 = (9) \cdot (\frac{1}{6}) + b$

Step 2.4

Rewrite the equation as $(9) \cdot (\frac{1}{6}) + b = - 1$ .

$(9) \cdot (\frac{1}{6}) + b = - 1$

Step 2.5

Simplify each term.

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Step 2.5.1

Cancel the common factor of $3$ .

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Step 2.5.1.1

Factor $3$ out of $9$ .

$3 (3) \cdot \frac{1}{6} + b = - 1$

Step 2.5.1.2

Factor $3$ out of $6$ .

$3 \cdot 3 \cdot \frac{1}{3 \cdot 2} + b = - 1$

Step 2.5.1.3

Cancel the common factor.

$3 \cdot 3 \cdot \frac{1}{3 \cdot 2} + b = - 1$

Step 2.5.1.4

Rewrite the expression.

$3 \cdot \frac{1}{2} + b = - 1$

Step 2.5.2

Combine $3$ and $\frac{1}{2}$ .

$\frac{3}{2} + b = - 1$

Step 2.6

Move all terms not containing $b$ to the right side of the equation.

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Step 2.6.1

Subtract $\frac{3}{2}$ from both sides of the equation.

$b = - 1 - \frac{3}{2}$

Step 2.6.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$b = - 1 \cdot \frac{2}{2} - \frac{3}{2}$

Step 2.6.3

Combine $- 1$ and $\frac{2}{2}$ .

$b = \frac{- 1 \cdot 2}{2} - \frac{3}{2}$

Step 2.6.4

Combine the numerators over the common denominator.

$b = \frac{- 1 \cdot 2 - 3}{2}$

Step 2.6.5

Simplify the numerator.

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Step 2.6.5.1

Multiply $- 1$ by $2$ .

$b = \frac{- 2 - 3}{2}$

Step 2.6.5.2

Subtract $3$ from $- 2$ .

$b = \frac{- 5}{2}$

Step 2.6.6

Move the negative in front of the fraction.

$b = - \frac{5}{2}$

Step 3

List the slope and y-intercept.

Slope: $9$

y-intercept: $(0, - \frac{5}{2})$

Step 4