Pre-Algebra Examples

$(12, - 2)$ , $(- 24, 6)$

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.

$m = \frac{6 - (- 2)}{- 24 - (12)}$

Step 1.4

Simplify.

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Step 1.4.1

Cancel the common factor of $6 - (- 2)$ and $- 24 - (12)$ .

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Step 1.4.1.1

Rewrite $- 24$ as $- 1 (24)$ .

$m = \frac{6 - (- 2)}{- 1 \cdot 24 - (12)}$

Step 1.4.1.2

Factor $- 1$ out of $- 1 (24) - (12)$ .

$m = \frac{6 - (- 2)}{- 1 (24 + 12)}$

Step 1.4.1.3

Reorder terms.

$m = \frac{6 - 2 \cdot - 1}{- 1 (24 + 12)}$

Step 1.4.1.4

Factor $2$ out of $6$ .

$m = \frac{2 (3) - 2 \cdot - 1}{- 1 (24 + 12)}$

Step 1.4.1.5

Factor $2$ out of $- 2 \cdot - 1$ .

$m = \frac{2 (3) + 2 (1)}{- 1 (24 + 12)}$

Step 1.4.1.6

Factor $2$ out of $2 (3) + 2 (- - 1)$ .

$m = \frac{2 (3 + 1)}{- 1 (24 + 12)}$

Step 1.4.1.7

Cancel the common factors.

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Step 1.4.1.7.1

Factor $2$ out of $- 1 (24 + 12)$ .

$m = \frac{2 (3 + 1)}{2 (- 1 (12 + 6))}$

Step 1.4.1.7.2

Cancel the common factor.

$m = \frac{2 (3 + 1)}{2 (- 1 (12 + 6))}$

Step 1.4.1.7.3

Rewrite the expression.

$m = \frac{3 + 1}{- 1 (12 + 6)}$

Step 1.4.2

Simplify the numerator.

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Step 1.4.2.1

Multiply $- 1$ by $- 1$ .

$m = \frac{3 + 1}{- 1 (12 + 6)}$

Step 1.4.2.2

Add $3$ and $1$ .

$m = \frac{4}{- 1 (12 + 6)}$

Step 1.4.3

Reduce the expression by cancelling the common factors.

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Step 1.4.3.1

Add $12$ and $6$ .

$m = \frac{4}{- 1 \cdot 18}$

Step 1.4.3.2

Multiply $- 1$ by $18$ .

$m = \frac{4}{- 18}$

Step 1.4.3.3

Cancel the common factor of $4$ and $- 18$ .

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Step 1.4.3.3.1

Factor $2$ out of $4$ .

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

Step 1.4.3.3.2

Cancel the common factors.

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Step 1.4.3.3.2.1

Factor $2$ out of $- 18$ .

$m = \frac{2 \cdot 2}{2 \cdot - 9}$

Step 1.4.3.3.2.2

Cancel the common factor.

$m = \frac{2 \cdot 2}{2 \cdot - 9}$

Step 1.4.3.3.2.3

Rewrite the expression.

$m = \frac{2}{- 9}$

Step 1.4.3.4

Move the negative in front of the fraction.

$m = - \frac{2}{9}$

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, $y = m x + b$ .

$y = (- \frac{2}{9}) \cdot x + b$

Step 2.2

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

$y = (- \frac{2}{9}) \cdot (12) + b$

Step 2.3

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

$- 2 = (- \frac{2}{9}) \cdot (12) + b$

Step 2.4

Rewrite the equation as $(- \frac{2}{9}) \cdot (12) + b = - 2$ .

$(- \frac{2}{9}) \cdot (12) + b = - 2$

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

Move the leading negative in $- \frac{2}{9}$ into the numerator.

$\frac{- 2}{9} \cdot 12 + b = - 2$

Step 2.5.1.2

Factor $3$ out of $9$ .

$\frac{- 2}{3 (3)} \cdot 12 + b = - 2$

Step 2.5.1.3

Factor $3$ out of $12$ .

$\frac{- 2}{3 \cdot 3} \cdot (3 \cdot 4) + b = - 2$

Step 2.5.1.4

Cancel the common factor.

$\frac{- 2}{3 \cdot 3} \cdot (3 \cdot 4) + b = - 2$

Step 2.5.1.5

Rewrite the expression.

$\frac{- 2}{3} \cdot 4 + b = - 2$

Step 2.5.2

Combine $\frac{- 2}{3}$ and $4$ .

$\frac{- 2 \cdot 4}{3} + b = - 2$

Step 2.5.3

Multiply $- 2$ by $4$ .

$\frac{- 8}{3} + b = - 2$

Step 2.5.4

Move the negative in front of the fraction.

$- \frac{8}{3} + b = - 2$

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 $\frac{8}{3}$ to both sides of the equation.

$b = - 2 + \frac{8}{3}$

Step 2.6.2

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$b = - 2 \cdot \frac{3}{3} + \frac{8}{3}$

Step 2.6.3

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

$b = \frac{- 2 \cdot 3}{3} + \frac{8}{3}$

Step 2.6.4

Combine the numerators over the common denominator.

$b = \frac{- 2 \cdot 3 + 8}{3}$

Step 2.6.5

Simplify the numerator.

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Step 2.6.5.1

Multiply $- 2$ by $3$ .

$b = \frac{- 6 + 8}{3}$

Step 2.6.5.2

Add $- 6$ and $8$ .

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

Step 3

List the slope and y-intercept.

Slope: $- \frac{2}{9}$

y-intercept: $(0, \frac{2}{3})$

Step 4