Find the Equation Using Point-Slope Formula (-8,8) , (1,-10)

$(- 8, 8)$ , $(1, - 10)$

Step 1

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

$m = \frac{- 10 - (8)}{1 - (- 8)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $8$ .

$m = \frac{- 10 - 8}{1 - (- 8)}$

Subtract $8$ from $- 10$ .

$m = \frac{- 18}{1 - (- 8)}$

Simplify the denominator.

Multiply $- 1$ by $- 8$ .

$m = \frac{- 18}{1 + 8}$

Add $1$ and $8$ .

$m = \frac{- 18}{9}$

Divide $- 18$ by $9$ .

$m = - 2$

Step 2

Use the slope $- 2$ and a given point $(- 8, 8)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (8) = - 2 \cdot (x - (- 8))$

Step 3

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

$y - 8 = - 2 \cdot (x + 8)$

Step 4

Solve for $y$ .

Simplify $- 2 \cdot (x + 8)$ .

Rewrite.

$y - 8 = 0 + 0 - 2 \cdot (x + 8)$

Simplify by adding zeros.

$y - 8 = - 2 \cdot (x + 8)$

Apply the distributive property.

$y - 8 = - 2 x - 2 \cdot 8$

Multiply $- 2$ by $8$ .

$y - 8 = - 2 x - 16$

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

Add $8$ to both sides of the equation.

$y = - 2 x - 16 + 8$

Add $- 16$ and $8$ .

$y = - 2 x - 8$

Step 5

List the equation in different forms.

Slope-intercept form:

$y = - 2 x - 8$

Point-slope form:

$y - 8 = - 2 \cdot (x + 8)$

Step 6

Find the Equation Using Point-Slope Formula (-8,8) , (1,-10)

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