Write in Slope-Intercept Form (-3,-8) and (2,7)

$(- 3, - 8)$ and $(2, 7)$

Find the slope of the line between $(- 3, - 8)$ and $(2, 7)$ 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.

$m = \frac{7 - (- 8)}{2 - (- 3)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 8$ .

$m = \frac{7 + 8}{2 - (- 3)}$

Add $7$ and $8$ .

$m = \frac{15}{2 - (- 3)}$

Simplify the denominator.

Multiply $- 1$ by $- 3$ .

$m = \frac{15}{2 + 3}$

Add $2$ and $3$ .

$m = \frac{15}{5}$

Divide $15$ by $5$ .

$m = 3$

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

$y - (- 8) = 3 \cdot (x - (- 3))$

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

$y + 8 = 3 \cdot (x + 3)$

Solve for $y$ .

Simplify $3 \cdot (x + 3)$ .

Rewrite.

$y + 8 = 0 + 0 + 3 \cdot (x + 3)$

Simplify by adding zeros.

$y + 8 = 3 \cdot (x + 3)$

Apply the distributive property.

$y + 8 = 3 x + 3 \cdot 3$

Multiply $3$ by $3$ .

$y + 8 = 3 x + 9$

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

Subtract $8$ from both sides of the equation.

$y = 3 x + 9 - 8$

Subtract $8$ from $9$ .

$y = 3 x + 1$

Write in Slope-Intercept Form (-3,-8) and (2,7)

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