Find the Equation Using Point-Slope Formula (-3,2) , (1,-10)

$(- 3, 2)$ , $(1, - 10)$

Step 1

Find the slope of the line between $(- 3, 2)$ and $(1, - 10)$ 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.

$m = \frac{- 10 - (2)}{1 - (- 3)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $2$ .

$m = \frac{- 10 - 2}{1 - (- 3)}$

Subtract $2$ from $- 10$ .

$m = \frac{- 12}{1 - (- 3)}$

Simplify the denominator.

Multiply $- 1$ by $- 3$ .

$m = \frac{- 12}{1 + 3}$

Add $1$ and $3$ .

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

Divide $- 12$ by $4$ .

$m = - 3$

Step 2

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

$y - (2) = - 3 \cdot (x - (- 3))$

Step 3

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

$y - 2 = - 3 \cdot (x + 3)$

Step 4

Solve for $y$ .

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

Rewrite.

$y - 2 = 0 + 0 - 3 \cdot (x + 3)$

Simplify by adding zeros.

$y - 2 = - 3 \cdot (x + 3)$

Apply the distributive property.

$y - 2 = - 3 x - 3 \cdot 3$

Multiply $- 3$ by $3$ .

$y - 2 = - 3 x - 9$

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

Add $2$ to both sides of the equation.

$y = - 3 x - 9 + 2$

Add $- 9$ and $2$ .

$y = - 3 x - 7$

Step 5

List the equation in different forms.

Slope-intercept form:

$y = - 3 x - 7$

Point-slope form:

$y - 2 = - 3 \cdot (x + 3)$

Step 6

Find the Equation Using Point-Slope Formula (-3,2) , (1,-10)

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