Write in Slope-Intercept Form (-4,-6) and (3,8)

$(- 4, - 6)$ and $(3, 8)$

Find the slope of the line between $(- 4, - 6)$ and $(3, 8)$ 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.

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

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 6$ .

$m = \frac{8 + 6}{3 - (- 4)}$

Add $8$ and $6$ .

$m = \frac{14}{3 - (- 4)}$

Simplify the denominator.

Multiply $- 1$ by $- 4$ .

$m = \frac{14}{3 + 4}$

Add $3$ and $4$ .

$m = \frac{14}{7}$

Divide $14$ by $7$ .

$m = 2$

Use the slope $2$ and a given point $(- 4, - 6)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 6) = 2 \cdot (x - (- 4))$

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

$y + 6 = 2 \cdot (x + 4)$

Solve for $y$ .

Simplify $2 \cdot (x + 4)$ .

Rewrite.

$y + 6 = 0 + 0 + 2 \cdot (x + 4)$

Simplify by adding zeros.

$y + 6 = 2 \cdot (x + 4)$

Apply the distributive property.

$y + 6 = 2 x + 2 \cdot 4$

Multiply $2$ by $4$ .

$y + 6 = 2 x + 8$

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

Subtract $6$ from both sides of the equation.

$y = 2 x + 8 - 6$

Subtract $6$ from $8$ .

$y = 2 x + 2$

Write in Slope-Intercept Form (-4,-6) and (3,8)

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