Pre-Algebra Examples

$(8, 10)$ , $(- 7, 14)$

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.

$m = \frac{14 - (10)}{- 7 - (8)}$

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 $10$ .

$m = \frac{14 - 10}{- 7 - (8)}$

Step 1.4.1.2

Subtract $10$ from $14$ .

$m = \frac{4}{- 7 - (8)}$

Step 1.4.2

Simplify the denominator.

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Step 1.4.2.1

Multiply $- 1$ by $8$ .

$m = \frac{4}{- 7 - 8}$

Step 1.4.2.2

Subtract $8$ from $- 7$ .

$m = \frac{4}{- 15}$

Step 1.4.3

Move the negative in front of the fraction.

$m = - \frac{4}{15}$

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, $y = m x + b$ .

$y = (- \frac{4}{15}) \cdot x + b$

Step 2.2

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

$y = (- \frac{4}{15}) \cdot (8) + b$

Step 2.3

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

$10 = (- \frac{4}{15}) \cdot (8) + b$

Step 2.4

Rewrite the equation as $(- \frac{4}{15}) \cdot (8) + b = 10$ .

$(- \frac{4}{15}) \cdot (8) + b = 10$

Step 2.5

Simplify each term.

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Step 2.5.1

Multiply $(- \frac{4}{15}) (8)$ .

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Step 2.5.1.1

Multiply $8$ by $- 1$ .

$- 8 (\frac{4}{15}) + b = 10$

Step 2.5.1.2

Combine $- 8$ and $\frac{4}{15}$ .

$\frac{- 8 \cdot 4}{15} + b = 10$

Step 2.5.1.3

Multiply $- 8$ by $4$ .

$\frac{- 32}{15} + b = 10$

Step 2.5.2

Move the negative in front of the fraction.

$- \frac{32}{15} + b = 10$

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 $\frac{32}{15}$ to both sides of the equation.

$b = 10 + \frac{32}{15}$

Step 2.6.2

To write $10$ as a fraction with a common denominator, multiply by $\frac{15}{15}$ .

$b = 10 \cdot \frac{15}{15} + \frac{32}{15}$

Step 2.6.3

Combine $10$ and $\frac{15}{15}$ .

$b = \frac{10 \cdot 15}{15} + \frac{32}{15}$

Step 2.6.4

Combine the numerators over the common denominator.

$b = \frac{10 \cdot 15 + 32}{15}$

Step 2.6.5

Simplify the numerator.

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Step 2.6.5.1

Multiply $10$ by $15$ .

$b = \frac{150 + 32}{15}$

Step 2.6.5.2

Add $150$ and $32$ .

$b = \frac{182}{15}$

Step 3

List the slope and y-intercept.

Slope: $- \frac{4}{15}$

y-intercept: $(0, \frac{182}{15})$

Step 4