Pre-Algebra Examples

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

Step 1

Find the slope of the line between $(- 8, - 6)$ and $(- 6, 8)$ using $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ , which is the change of $y$ over the change of $x$ .

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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.

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

Step 1.4

Simplify.

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Step 1.4.1

Reduce the expression by cancelling the common factors.

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Step 1.4.1.1

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

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Step 1.4.1.1.1

Rewrite $8$ as $- 1 (- 8)$ .

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

Step 1.4.1.1.2

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

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

Step 1.4.1.1.3

Reorder terms.

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

Step 1.4.1.1.4

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

$m = \frac{2 (- 1 (- 4 - 3))}{- 6 - 8 \cdot - 1}$

Step 1.4.1.1.5

Cancel the common factors.

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Step 1.4.1.1.5.1

Factor $2$ out of $- 6$ .

$m = \frac{2 (- 1 (- 4 - 3))}{2 (- 3) - 8 \cdot - 1}$

Step 1.4.1.1.5.2

Factor $2$ out of $- 8 \cdot - 1$ .

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

Step 1.4.1.1.5.3

Factor $2$ out of $2 (- 3) + 2 (- 4 \cdot - 1)$ .

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

Step 1.4.1.1.5.4

Cancel the common factor.

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

Step 1.4.1.1.5.5

Rewrite the expression.

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

Step 1.4.1.2

Subtract $3$ from $- 4$ .

$m = \frac{- 1 \cdot - 7}{- 3 - 4 \cdot - 1}$

Step 1.4.2

Simplify the denominator.

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Step 1.4.2.1

Multiply $- 4$ by $- 1$ .

$m = \frac{- 1 \cdot - 7}{- 3 + 4}$

Step 1.4.2.2

Add $- 3$ and $4$ .

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

Step 1.4.3

Simplify the expression.

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Step 1.4.3.1

Multiply $- 1$ by $- 7$ .

$m = \frac{7}{1}$

Step 1.4.3.2

Divide $7$ by $1$ .

$m = 7$

Step 2

Use the slope $7$ and a given point $(- 8, - 6)$ to substitute for $x_{1}$ and $y_{1}$ in the point-slope form $y - y_{1} = m (x - x_{1})$ , which is derived from the slope equation $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 6) = 7 \cdot (x - (- 8))$

Step 3

Simplify the equation and keep it in point-slope form.

$y + 6 = 7 \cdot (x + 8)$

Step 4

Solve for $y$ .

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Step 4.1

Simplify $7 \cdot (x + 8)$ .

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Step 4.1.1

Rewrite.

$y + 6 = 0 + 0 + 7 \cdot (x + 8)$

Step 4.1.2

Simplify by adding zeros.

$y + 6 = 7 \cdot (x + 8)$

Step 4.1.3

Apply the distributive property.

$y + 6 = 7 x + 7 \cdot 8$

Step 4.1.4

Multiply $7$ by $8$ .

$y + 6 = 7 x + 56$

Step 4.2

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

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Step 4.2.1

Subtract $6$ from both sides of the equation.

$y = 7 x + 56 - 6$

Step 4.2.2

Subtract $6$ from $56$ .

$y = 7 x + 50$

Step 5

List the equation in different forms.

Slope-intercept form:

$y = 7 x + 50$

Point-slope form:

$y + 6 = 7 \cdot (x + 8)$

Step 6