Write in Slope-Intercept Form (-5,-11) and (-2,1)

$(- 5, - 11)$ and $(- 2, 1)$

Find the slope of the line between $(- 5, - 11)$ and $(- 2, 1)$ 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.

$m = \frac{1 - (- 11)}{- 2 - (- 5)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 11$ .

$m = \frac{1 + 11}{- 2 - (- 5)}$

Add $1$ and $11$ .

$m = \frac{12}{- 2 - (- 5)}$

Simplify the denominator.

Multiply $- 1$ by $- 5$ .

$m = \frac{12}{- 2 + 5}$

Add $- 2$ and $5$ .

$m = \frac{12}{3}$

Divide $12$ by $3$ .

$m = 4$

Use the slope $4$ and a given point $(- 5, - 11)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 11) = 4 \cdot (x - (- 5))$

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

$y + 11 = 4 \cdot (x + 5)$

Solve for $y$ .

Simplify $4 \cdot (x + 5)$ .

Rewrite.

$y + 11 = 0 + 0 + 4 \cdot (x + 5)$

Simplify by adding zeros.

$y + 11 = 4 \cdot (x + 5)$

Apply the distributive property.

$y + 11 = 4 x + 4 \cdot 5$

Multiply $4$ by $5$ .

$y + 11 = 4 x + 20$

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

Subtract $11$ from both sides of the equation.

$y = 4 x + 20 - 11$

Subtract $11$ from $20$ .

$y = 4 x + 9$

Write in Slope-Intercept Form (-5,-11) and (-2,1)

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