Write in Slope-Intercept Form (1,-9) and (-3,-9)

$(1, - 9)$ and $(- 3, - 9)$

Find the slope of the line between $(1, - 9)$ and $(- 3, - 9)$ 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.

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

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 9$ .

$m = \frac{- 9 + 9}{- 3 - (1)}$

Add $- 9$ and $9$ .

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

Simplify the denominator.

Multiply $- 1$ by $1$ .

$m = \frac{0}{- 3 - 1}$

Subtract $1$ from $- 3$ .

$m = \frac{0}{- 4}$

Divide $0$ by $- 4$ .

$m = 0$

Use the slope $0$ and a given point $(1, - 9)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 9) = 0 \cdot (x - (1))$

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

$y + 9 = 0 \cdot (x - 1)$

Solve for $y$ .

Multiply $0$ by $x - 1$ .

$y + 9 = 0$

Subtract $9$ from both sides of the equation.

$y = - 9$

Write in Slope-Intercept Form (1,-9) and (-3,-9)

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