Write in Slope-Intercept Form (-2,-8) and (6,4)

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

Step 1

Find the slope of the line between $(- 2, - 8)$ and $(6, 4)$ 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.

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

Simplify.

Reduce the expression by cancelling the common factors.

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

Rewrite $4$ as $- 1 (- 4)$ .

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

Factor $- 1$ out of $- 1 (- 4) - (- 8)$ .

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

Reorder terms.

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

Factor $2$ out of $- 1 (- 4 - 8)$ .

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

Cancel the common factors.

Factor $2$ out of $6$ .

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

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

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Subtract $4$ from $- 2$ .

$m = \frac{- 1 \cdot - 6}{3 + 1}$

Simplify the denominator.

Multiply $- 1$ by $- 1$ .

$m = \frac{- 1 \cdot - 6}{3 + 1}$

Add $3$ and $1$ .

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

Reduce the expression by cancelling the common factors.

Multiply $- 1$ by $- 6$ .

$m = \frac{6}{4}$

Cancel the common factor of $6$ and $4$ .

Factor $2$ out of $6$ .

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

Cancel the common factors.

Factor $2$ out of $4$ .

$m = \frac{2 \cdot 3}{2 \cdot 2}$

Cancel the common factor.

$m = \frac{2 \cdot 3}{2 \cdot 2}$

Rewrite the expression.

$m = \frac{3}{2}$

Step 2

Use the slope $\frac{3}{2}$ and a given point $(- 2, - 8)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 8) = \frac{3}{2} \cdot (x - (- 2))$

Step 3

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

$y + 8 = \frac{3}{2} \cdot (x + 2)$

Step 4

Write the equation in $y = m x + b$ form.

Solve for $y$ .

Simplify $\frac{3}{2} \cdot (x + 2)$ .

Rewrite.

$y + 8 = 0 + 0 + \frac{3}{2} \cdot (x + 2)$

Simplify by adding zeros.

$y + 8 = \frac{3}{2} \cdot (x + 2)$

Apply the distributive property.

$y + 8 = \frac{3}{2} x + \frac{3}{2} \cdot 2$

Combine $\frac{3}{2}$ and $x$ .

$y + 8 = \frac{3 x}{2} + \frac{3}{2} \cdot 2$

Cancel the common factor of $2$ .

Cancel the common factor.

$y + 8 = \frac{3 x}{2} + \frac{3}{2} \cdot 2$

Rewrite the expression.

$y + 8 = \frac{3 x}{2} + 3$

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

Subtract $8$ from both sides of the equation.

$y = \frac{3 x}{2} + 3 - 8$

Subtract $8$ from $3$ .

$y = \frac{3 x}{2} - 5$

Reorder terms.

$y = \frac{3}{2} x - 5$

Step 5

Write in Slope-Intercept Form (-2,-8) and (6,4)

Related Questions

Support LCMGCF.com by disabling your adblocker.