Find the Equation Using Point-Slope Formula (-3,-7) , (8,-7)

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

Step 1

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

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

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 7$ .

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

Add $- 7$ and $7$ .

$m = \frac{0}{8 - (- 3)}$

Simplify the denominator.

Multiply $- 1$ by $- 3$ .

$m = \frac{0}{8 + 3}$

Add $8$ and $3$ .

$m = \frac{0}{11}$

Divide $0$ by $11$ .

$m = 0$

Step 2

Use the slope $0$ and a given point $(- 3, - 7)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 7) = 0 \cdot (x - (- 3))$

Step 3

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

$y + 7 = 0 \cdot (x + 3)$

Step 4

Solve for $y$ .

Multiply $0$ by $x + 3$ .

$y + 7 = 0$

Subtract $7$ from both sides of the equation.

$y = - 7$

Step 5

List the equation in different forms.

Slope-intercept form:

$y = - 7$

Point-slope form:

$y + 7 = 0 \cdot (x + 3)$

Step 6

Find the Equation Using Point-Slope Formula (-3,-7) , (8,-7)

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