Write in Slope-Intercept Form (-9,-9) and (-6,0)

$(- 9, - 9)$ and $(- 6, 0)$

Step 1

Find the slope of the line between $(- 9, - 9)$ and $(- 6, 0)$ 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.

$m = \frac{0 - (- 9)}{- 6 - (- 9)}$

Simplify.

Reduce the expression by cancelling the common factors.

Cancel the common factor of $0 - (- 9)$ and $- 6 - (- 9)$ .

Rewrite $0$ as $- 1 (0)$ .

$m = \frac{- 1 \cdot 0 - (- 9)}{- 6 - (- 9)}$

Factor $- 1$ out of $- 1 (0) - (- 9)$ .

$m = \frac{- 1 (0 - 9)}{- 6 - (- 9)}$

Reorder terms.

$m = \frac{- 1 (0 - 9)}{- 6 - 9 \cdot - 1}$

Factor $3$ out of $- 1 (0 - 9)$ .

$m = \frac{3 (- 1 (0 - 3))}{- 6 - 9 \cdot - 1}$

Cancel the common factors.

Factor $3$ out of $- 6$ .

$m = \frac{3 (- 1 (0 - 3))}{3 (- 2) - 9 \cdot - 1}$

Factor $3$ out of $- 9 \cdot - 1$ .

$m = \frac{3 (- 1 (0 - 3))}{3 (- 2) + 3 (- 3 \cdot - 1)}$

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

$m = \frac{3 (- 1 (0 - 3))}{3 (- 2 - 3 \cdot - 1)}$

Cancel the common factor.

$m = \frac{3 (- 1 (0 - 3))}{3 (- 2 - 3 \cdot - 1)}$

Rewrite the expression.

$m = \frac{- 1 (0 - 3)}{- 2 - 3 \cdot - 1}$

Subtract $3$ from $0$ .

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

Simplify the denominator.

Multiply $- 3$ by $- 1$ .

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

Add $- 2$ and $3$ .

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

Simplify the expression.

Multiply $- 1$ by $- 3$ .

$m = \frac{3}{1}$

Divide $3$ by $1$ .

$m = 3$

Step 2

Use the slope $3$ and a given point $(- 9, - 9)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 9) = 3 \cdot (x - (- 9))$

Step 3

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

$y + 9 = 3 \cdot (x + 9)$

Step 4

Solve for $y$ .

Simplify $3 \cdot (x + 9)$ .

Rewrite.

$y + 9 = 0 + 0 + 3 \cdot (x + 9)$

Simplify by adding zeros.

$y + 9 = 3 \cdot (x + 9)$

Apply the distributive property.

$y + 9 = 3 x + 3 \cdot 9$

Multiply $3$ by $9$ .

$y + 9 = 3 x + 27$

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

Subtract $9$ from both sides of the equation.

$y = 3 x + 27 - 9$

Subtract $9$ from $27$ .

$y = 3 x + 18$

Step 5

Write in Slope-Intercept Form (-9,-9) and (-6,0)

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