Pre-Algebra Examples

$(8, - 4)$ , $(- 6, 8)$

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.

$m = \frac{8 - (- 4)}{- 6 - (8)}$

Step 1.4

Simplify.

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Step 1.4.1

Cancel the common factor of $8 - (- 4)$ and $- 6 - (8)$ .

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Step 1.4.1.1

Rewrite $- 6$ as $- 1 (6)$ .

$m = \frac{8 - (- 4)}{- 1 \cdot 6 - (8)}$

Step 1.4.1.2

Factor $- 1$ out of $- 1 (6) - (8)$ .

$m = \frac{8 - (- 4)}{- 1 (6 + 8)}$

Step 1.4.1.3

Reorder terms.

$m = \frac{8 - 4 \cdot - 1}{- 1 (6 + 8)}$

Step 1.4.1.4

Factor $2$ out of $8$ .

$m = \frac{2 (4) - 4 \cdot - 1}{- 1 (6 + 8)}$

Step 1.4.1.5

Factor $2$ out of $- 4 \cdot - 1$ .

$m = \frac{2 (4) + 2 (- 2 \cdot - 1)}{- 1 (6 + 8)}$

Step 1.4.1.6

Factor $2$ out of $2 (4) + 2 (- 2 \cdot - 1)$ .

$m = \frac{2 (4 - 2 \cdot - 1)}{- 1 (6 + 8)}$

Step 1.4.1.7

Cancel the common factors.

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Step 1.4.1.7.1

Factor $2$ out of $- 1 (6 + 8)$ .

$m = \frac{2 (4 - 2 \cdot - 1)}{2 (- 1 (3 + 4))}$

Step 1.4.1.7.2

Cancel the common factor.

$m = \frac{2 (4 - 2 \cdot - 1)}{2 (- 1 (3 + 4))}$

Step 1.4.1.7.3

Rewrite the expression.

$m = \frac{4 - 2 \cdot - 1}{- 1 (3 + 4)}$

Step 1.4.2

Simplify the numerator.

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Step 1.4.2.1

Multiply $- 2$ by $- 1$ .

$m = \frac{4 + 2}{- 1 (3 + 4)}$

Step 1.4.2.2

Add $4$ and $2$ .

$m = \frac{6}{- 1 (3 + 4)}$

Step 1.4.3

Simplify the expression.

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Step 1.4.3.1

Add $3$ and $4$ .

$m = \frac{6}{- 1 \cdot 7}$

Step 1.4.3.2

Multiply $- 1$ by $7$ .

$m = \frac{6}{- 7}$

Step 1.4.3.3

Move the negative in front of the fraction.

$m = - \frac{6}{7}$

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, $y = m x + b$ .

$y = (- \frac{6}{7}) \cdot x + b$

Step 2.2

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

$y = (- \frac{6}{7}) \cdot (8) + b$

Step 2.3

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

$- 4 = (- \frac{6}{7}) \cdot (8) + b$

Step 2.4

Rewrite the equation as $(- \frac{6}{7}) \cdot (8) + b = - 4$ .

$(- \frac{6}{7}) \cdot (8) + b = - 4$

Step 2.5

Simplify each term.

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Step 2.5.1

Multiply $(- \frac{6}{7}) (8)$ .

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Step 2.5.1.1

Multiply $8$ by $- 1$ .

$- 8 (\frac{6}{7}) + b = - 4$

Step 2.5.1.2

Combine $- 8$ and $\frac{6}{7}$ .

$\frac{- 8 \cdot 6}{7} + b = - 4$

Step 2.5.1.3

Multiply $- 8$ by $6$ .

$\frac{- 48}{7} + b = - 4$

Step 2.5.2

Move the negative in front of the fraction.

$- \frac{48}{7} + b = - 4$

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 $\frac{48}{7}$ to both sides of the equation.

$b = - 4 + \frac{48}{7}$

Step 2.6.2

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$b = - 4 \cdot \frac{7}{7} + \frac{48}{7}$

Step 2.6.3

Combine $- 4$ and $\frac{7}{7}$ .

$b = \frac{- 4 \cdot 7}{7} + \frac{48}{7}$

Step 2.6.4

Combine the numerators over the common denominator.

$b = \frac{- 4 \cdot 7 + 48}{7}$

Step 2.6.5

Simplify the numerator.

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Step 2.6.5.1

Multiply $- 4$ by $7$ .

$b = \frac{- 28 + 48}{7}$

Step 2.6.5.2

Add $- 28$ and $48$ .

$b = \frac{20}{7}$

Step 3

List the slope and y-intercept.

Slope: $- \frac{6}{7}$

y-intercept: $(0, \frac{20}{7})$

Step 4