Find the Equation Using Point-Slope Formula (-4,9) , (2,-3)

$(- 4, 9)$ , $(2, - 3)$

Step 1

Find the slope of the line between $(- 4, 9)$ and $(2, - 3)$ 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.

$m = \frac{- 3 - (9)}{2 - (- 4)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $9$ .

$m = \frac{- 3 - 9}{2 - (- 4)}$

Subtract $9$ from $- 3$ .

$m = \frac{- 12}{2 - (- 4)}$

Simplify the denominator.

Multiply $- 1$ by $- 4$ .

$m = \frac{- 12}{2 + 4}$

Add $2$ and $4$ .

$m = \frac{- 12}{6}$

Divide $- 12$ by $6$ .

$m = - 2$

Step 2

Use the slope $- 2$ and a given point $(- 4, 9)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (9) = - 2 \cdot (x - (- 4))$

Step 3

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

$y - 9 = - 2 \cdot (x + 4)$

Step 4

Solve for $y$ .

Simplify $- 2 \cdot (x + 4)$ .

Rewrite.

$y - 9 = 0 + 0 - 2 \cdot (x + 4)$

Simplify by adding zeros.

$y - 9 = - 2 \cdot (x + 4)$

Apply the distributive property.

$y - 9 = - 2 x - 2 \cdot 4$

Multiply $- 2$ by $4$ .

$y - 9 = - 2 x - 8$

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

Add $9$ to both sides of the equation.

$y = - 2 x - 8 + 9$

Add $- 8$ and $9$ .

$y = - 2 x + 1$

Step 5

List the equation in different forms.

Slope-intercept form:

$y = - 2 x + 1$

Point-slope form:

$y - 9 = - 2 \cdot (x + 4)$

Step 6

Find the Equation Using Point-Slope Formula (-4,9) , (2,-3)

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