Find the Equation Using Point-Slope Formula (-9,6) , (-7,-8)

$(- 9, 6)$ , $(- 7, - 8)$

Step 1

Find the slope of the line between $(- 9, 6)$ and $(- 7, - 8)$ 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.

$m = \frac{- 8 - (6)}{- 7 - (- 9)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $6$ .

$m = \frac{- 8 - 6}{- 7 - (- 9)}$

Subtract $6$ from $- 8$ .

$m = \frac{- 14}{- 7 - (- 9)}$

Simplify the denominator.

Multiply $- 1$ by $- 9$ .

$m = \frac{- 14}{- 7 + 9}$

Add $- 7$ and $9$ .

$m = \frac{- 14}{2}$

Divide $- 14$ by $2$ .

$m = - 7$

Step 2

Use the slope $- 7$ and a given point $(- 9, 6)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (6) = - 7 \cdot (x - (- 9))$

Step 3

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

$y - 6 = - 7 \cdot (x + 9)$

Step 4

Solve for $y$ .

Simplify $- 7 \cdot (x + 9)$ .

Rewrite.

$y - 6 = 0 + 0 - 7 \cdot (x + 9)$

Simplify by adding zeros.

$y - 6 = - 7 \cdot (x + 9)$

Apply the distributive property.

$y - 6 = - 7 x - 7 \cdot 9$

Multiply $- 7$ by $9$ .

$y - 6 = - 7 x - 63$

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

Add $6$ to both sides of the equation.

$y = - 7 x - 63 + 6$

Add $- 63$ and $6$ .

$y = - 7 x - 57$

Step 5

List the equation in different forms.

Slope-intercept form:

$y = - 7 x - 57$

Point-slope form:

$y - 6 = - 7 \cdot (x + 9)$

Step 6

Find the Equation Using Point-Slope Formula (-9,6) , (-7,-8)

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