Write in y=mx+b Form (-8,-2) and (-4,6)

$(- 8, - 2)$ and $(- 4, 6)$

Step 1

Find the slope of the line between $(- 8, - 2)$ and $(- 4, 6)$ using $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ , which is the change of $y$ over the change of $x$ .

Slope is equal to the change in $y$ over the change in $x$ , or rise over run.

$m = \frac{change in y}{change in x}$

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).

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

Substitute in the values of $x$ and $y$ into the equation to find the slope.

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

Simplify.

Reduce the expression by cancelling the common factors.

Cancel the common factor of $6 - (- 2)$ and $- 4 - (- 8)$ .

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

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

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

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

Reorder terms.

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

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

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

Cancel the common factors.

Factor $2$ out of $- 4$ .

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

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

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Subtract $1$ from $- 3$ .

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

Simplify the denominator.

Multiply $- 4$ by $- 1$ .

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

Add $- 2$ and $4$ .

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

Simplify the expression.

Multiply $- 1$ by $- 4$ .

$m = \frac{4}{2}$

Divide $4$ by $2$ .

$m = 2$

Step 2

Use the slope $2$ and a given point $(- 8, - 2)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 2) = 2 \cdot (x - (- 8))$

Step 3

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

$y + 2 = 2 \cdot (x + 8)$

Step 4

Solve for $y$ .

Simplify $2 \cdot (x + 8)$ .

Rewrite.

$y + 2 = 0 + 0 + 2 \cdot (x + 8)$

Simplify by adding zeros.

$y + 2 = 2 \cdot (x + 8)$

Apply the distributive property.

$y + 2 = 2 x + 2 \cdot 8$

Multiply $2$ by $8$ .

$y + 2 = 2 x + 16$

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

Subtract $2$ from both sides of the equation.

$y = 2 x + 16 - 2$

Subtract $2$ from $16$ .

$y = 2 x + 14$

Step 5

Write in y=mx+b Form (-8,-2) and (-4,6)

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