Pre-Algebra Examples

$(- \frac{6}{5}, - \frac{9}{10})$ , $(\frac{8}{3}, - \frac{9}{10})$

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.

$m = \frac{- \frac{9}{10} - (- \frac{9}{10})}{\frac{8}{3} - (- \frac{6}{5})}$

Step 1.4

Simplify.

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Step 1.4.1

Multiply the numerator and denominator of the fraction by $30$ .

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Step 1.4.1.1

Multiply $\frac{- \frac{9}{10} - - \frac{9}{10}}{\frac{8}{3} - - \frac{6}{5}}$ by $\frac{30}{30}$ .

$m = \frac{30}{30} \cdot \frac{- \frac{9}{10} + \frac{9}{10}}{\frac{8}{3} + \frac{6}{5}}$

Step 1.4.1.2

Combine.

$m = \frac{30 (- \frac{9}{10} + \frac{9}{10})}{30 (\frac{8}{3} + \frac{6}{5})}$

Step 1.4.2

Apply the distributive property.

$m = \frac{30 (- \frac{9}{10}) + 30 (\frac{9}{10})}{30 (\frac{8}{3}) + 30 (\frac{6}{5})}$

Step 1.4.3

Simplify by cancelling.

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Step 1.4.3.1

Cancel the common factor of $10$ .

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Step 1.4.3.1.1

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

$m = \frac{30 (\frac{- 9}{10}) + 30 (\frac{9}{10})}{30 (\frac{8}{3}) + 30 (\frac{6}{5})}$

Step 1.4.3.1.2

Factor $10$ out of $30$ .

$m = \frac{10 (3) (\frac{- 9}{10}) + 30 (\frac{9}{10})}{30 (\frac{8}{3}) + 30 (\frac{6}{5})}$

Step 1.4.3.1.3

Cancel the common factor.

$m = \frac{10 \cdot (3 (\frac{- 9}{10})) + 30 (\frac{9}{10})}{30 (\frac{8}{3}) + 30 (\frac{6}{5})}$

Step 1.4.3.1.4

Rewrite the expression.

$m = \frac{3 \cdot - 9 + 30 (\frac{9}{10})}{30 (\frac{8}{3}) + 30 (\frac{6}{5})}$

Step 1.4.3.2

Multiply $3$ by $- 9$ .

$m = \frac{- 27 + 30 (\frac{9}{10})}{30 (\frac{8}{3}) + 30 (\frac{6}{5})}$

Step 1.4.3.3

Cancel the common factor of $3$ .

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Step 1.4.3.3.1

Factor $3$ out of $30$ .

$m = \frac{- 27 + 30 (\frac{9}{10})}{3 (10) (\frac{8}{3}) + 30 (\frac{6}{5})}$

Step 1.4.3.3.2

Cancel the common factor.

$m = \frac{- 27 + 30 (\frac{9}{10})}{3 \cdot (10 (\frac{8}{3})) + 30 (\frac{6}{5})}$

Step 1.4.3.3.3

Rewrite the expression.

$m = \frac{- 27 + 30 (\frac{9}{10})}{10 \cdot 8 + 30 (\frac{6}{5})}$

Step 1.4.3.4

Multiply $10$ by $8$ .

$m = \frac{- 27 + 30 (\frac{9}{10})}{80 + 30 (\frac{6}{5})}$

Step 1.4.4

Simplify the numerator.

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Step 1.4.4.1

Multiply $- - \frac{9}{10}$ .

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Step 1.4.4.1.1

Multiply $- 1$ by $- 1$ .

$m = \frac{- 27 + 30 (1 (\frac{9}{10}))}{80 + 30 (\frac{6}{5})}$

Step 1.4.4.1.2

Multiply $\frac{9}{10}$ by $1$ .

$m = \frac{- 27 + 30 (\frac{9}{10})}{80 + 30 (\frac{6}{5})}$

Step 1.4.4.2

Cancel the common factor of $10$ .

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Step 1.4.4.2.1

Factor $10$ out of $30$ .

$m = \frac{- 27 + 10 (3) (\frac{9}{10})}{80 + 30 (\frac{6}{5})}$

Step 1.4.4.2.2

Cancel the common factor.

$m = \frac{- 27 + 10 \cdot (3 (\frac{9}{10}))}{80 + 30 (\frac{6}{5})}$

Step 1.4.4.2.3

Rewrite the expression.

$m = \frac{- 27 + 3 \cdot 9}{80 + 30 (\frac{6}{5})}$

Step 1.4.4.3

Multiply $3$ by $9$ .

$m = \frac{- 27 + 27}{80 + 30 (\frac{6}{5})}$

Step 1.4.4.4

Add $- 27$ and $27$ .

$m = \frac{0}{80 + 30 (\frac{6}{5})}$

Step 1.4.5

Simplify the denominator.

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Step 1.4.5.1

Multiply $- - \frac{6}{5}$ .

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Step 1.4.5.1.1

Multiply $- 1$ by $- 1$ .

$m = \frac{0}{80 + 30 (1 (\frac{6}{5}))}$

Step 1.4.5.1.2

Multiply $\frac{6}{5}$ by $1$ .

$m = \frac{0}{80 + 30 (\frac{6}{5})}$

Step 1.4.5.2

Cancel the common factor of $5$ .

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Step 1.4.5.2.1

Factor $5$ out of $30$ .

$m = \frac{0}{80 + 5 (6) (\frac{6}{5})}$

Step 1.4.5.2.2

Cancel the common factor.

$m = \frac{0}{80 + 5 \cdot (6 (\frac{6}{5}))}$

Step 1.4.5.2.3

Rewrite the expression.

$m = \frac{0}{80 + 6 \cdot 6}$

Step 1.4.5.3

Multiply $6$ by $6$ .

$m = \frac{0}{80 + 36}$

Step 1.4.5.4

Add $80$ and $36$ .

$m = \frac{0}{116}$

Step 1.4.6

Divide $0$ by $116$ .

$m = 0$

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, $y = m x + b$ .

$y = (0) \cdot x + b$

Step 2.2

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

$y = (0) \cdot (- \frac{6}{5}) + b$

Step 2.3

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

$- \frac{9}{10} = (0) \cdot (- \frac{6}{5}) + b$

Step 2.4

Rewrite the equation as $(0) \cdot (- \frac{6}{5}) + b = - \frac{9}{10}$ .

$(0) \cdot (- \frac{6}{5}) + b = - \frac{9}{10}$

Step 2.5

Simplify $(0) \cdot (- \frac{6}{5}) + b$ .

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Step 2.5.1

Multiply $(0) (- \frac{6}{5})$ .

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Step 2.5.1.1

Multiply $- 1$ by $0$ .

$0 (\frac{6}{5}) + b = - \frac{9}{10}$

Step 2.5.1.2

Multiply $0$ by $\frac{6}{5}$ .

$0 + b = - \frac{9}{10}$

Step 2.5.2

Add $0$ and $b$ .

$b = - \frac{9}{10}$

Step 3

List the slope and y-intercept.

Slope: $0$

y-intercept: $(0, - \frac{9}{10})$

Step 4