Pre-Algebra Examples

$(- 1, - 13)$ , $(- 14, - 17)$

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.

$m = \frac{- 17 - (- 13)}{- 14 - (- 1)}$

Step 1.4

Simplify.

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Step 1.4.1

Simplify the numerator.

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Step 1.4.1.1

Multiply $- 1$ by $- 13$ .

$m = \frac{- 17 + 13}{- 14 - (- 1)}$

Step 1.4.1.2

Add $- 17$ and $13$ .

$m = \frac{- 4}{- 14 - (- 1)}$

Step 1.4.2

Simplify the denominator.

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Step 1.4.2.1

Multiply $- 1$ by $- 1$ .

$m = \frac{- 4}{- 14 + 1}$

Step 1.4.2.2

Add $- 14$ and $1$ .

$m = \frac{- 4}{- 13}$

Step 1.4.3

Dividing two negative values results in a positive value.

$m = \frac{4}{13}$

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, $y = m x + b$ .

$y = (\frac{4}{13}) x + b$

Step 2.2

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

$y = (\frac{4}{13}) \cdot (- 1) + b$

Step 2.3

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

$- 13 = (\frac{4}{13}) \cdot (- 1) + b$

Step 2.4

Rewrite the equation as $(\frac{4}{13}) \cdot (- 1) + b = - 13$ .

$(\frac{4}{13}) \cdot (- 1) + b = - 13$

Step 2.5

Simplify each term.

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Step 2.5.1

Multiply $(\frac{4}{13}) (- 1)$ .

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Step 2.5.1.1

Combine $\frac{4}{13}$ and $- 1$ .

$\frac{4 \cdot - 1}{13} + b = - 13$

Step 2.5.1.2

Multiply $4$ by $- 1$ .

$\frac{- 4}{13} + b = - 13$

Step 2.5.2

Move the negative in front of the fraction.

$- \frac{4}{13} + b = - 13$

Step 2.6

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

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Step 2.6.1

Add $\frac{4}{13}$ to both sides of the equation.

$b = - 13 + \frac{4}{13}$

Step 2.6.2

To write $- 13$ as a fraction with a common denominator, multiply by $\frac{13}{13}$ .

$b = - 13 \cdot \frac{13}{13} + \frac{4}{13}$

Step 2.6.3

Combine $- 13$ and $\frac{13}{13}$ .

$b = \frac{- 13 \cdot 13}{13} + \frac{4}{13}$

Step 2.6.4

Combine the numerators over the common denominator.

$b = \frac{- 13 \cdot 13 + 4}{13}$

Step 2.6.5

Simplify the numerator.

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Step 2.6.5.1

Multiply $- 13$ by $13$ .

$b = \frac{- 169 + 4}{13}$

Step 2.6.5.2

Add $- 169$ and $4$ .

$b = \frac{- 165}{13}$

Step 2.6.6

Move the negative in front of the fraction.

$b = - \frac{165}{13}$

Step 3

List the slope and y-intercept.

Slope: $\frac{4}{13}$

y-intercept: $(0, - \frac{165}{13})$

Step 4