Pre-Algebra Examples

$(6, 7)$ , $(- 6, 8)$

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.

$m = \frac{8 - (7)}{- 6 - (6)}$

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 $7$ .

$m = \frac{8 - 7}{- 6 - (6)}$

Step 1.4.1.2

Subtract $7$ from $8$ .

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

Step 1.4.2

Simplify the denominator.

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Step 1.4.2.1

Multiply $- 1$ by $6$ .

$m = \frac{1}{- 6 - 6}$

Step 1.4.2.2

Subtract $6$ from $- 6$ .

$m = \frac{1}{- 12}$

Step 1.4.3

Move the negative in front of the fraction.

$m = - \frac{1}{12}$

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, $y = m x + b$ .

$y = (- \frac{1}{12}) \cdot x + b$

Step 2.2

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

$y = (- \frac{1}{12}) \cdot (6) + b$

Step 2.3

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

$7 = (- \frac{1}{12}) \cdot (6) + b$

Step 2.4

Rewrite the equation as $(- \frac{1}{12}) \cdot (6) + b = 7$ .

$(- \frac{1}{12}) \cdot (6) + b = 7$

Step 2.5

Simplify each term.

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Step 2.5.1

Cancel the common factor of $6$ .

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Step 2.5.1.1

Move the leading negative in $- \frac{1}{12}$ into the numerator.

$\frac{- 1}{12} \cdot 6 + b = 7$

Step 2.5.1.2

Factor $6$ out of $12$ .

$\frac{- 1}{6 (2)} \cdot 6 + b = 7$

Step 2.5.1.3

Cancel the common factor.

$\frac{- 1}{6 \cdot 2} \cdot 6 + b = 7$

Step 2.5.1.4

Rewrite the expression.

$\frac{- 1}{2} + b = 7$

Step 2.5.2

Move the negative in front of the fraction.

$- \frac{1}{2} + b = 7$

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 $\frac{1}{2}$ to both sides of the equation.

$b = 7 + \frac{1}{2}$

Step 2.6.2

To write $7$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$b = 7 \cdot \frac{2}{2} + \frac{1}{2}$

Step 2.6.3

Combine $7$ and $\frac{2}{2}$ .

$b = \frac{7 \cdot 2}{2} + \frac{1}{2}$

Step 2.6.4

Combine the numerators over the common denominator.

$b = \frac{7 \cdot 2 + 1}{2}$

Step 2.6.5

Simplify the numerator.

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Step 2.6.5.1

Multiply $7$ by $2$ .

$b = \frac{14 + 1}{2}$

Step 2.6.5.2

Add $14$ and $1$ .

$b = \frac{15}{2}$

Step 3

List the slope and y-intercept.

Slope: $- \frac{1}{12}$

y-intercept: $(0, \frac{15}{2})$

Step 4