Find the Equation Using Point-Slope Formula (-8,1) , (0,-2)

$(- 8, 1)$ , $(0, - 2)$

Step 1

Find the slope of the line between $(- 8, 1)$ and $(0, - 2)$ 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.

$m = \frac{- 2 - (1)}{0 - (- 8)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $1$ .

$m = \frac{- 2 - 1}{0 - (- 8)}$

Subtract $1$ from $- 2$ .

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

Simplify the denominator.

Multiply $- 1$ by $- 8$ .

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

Add $0$ and $8$ .

$m = \frac{- 3}{8}$

Move the negative in front of the fraction.

$m = - \frac{3}{8}$

Step 2

Use the slope $- \frac{3}{8}$ and a given point $(- 8, 1)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (1) = - \frac{3}{8} \cdot (x - (- 8))$

Step 3

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

$y - 1 = - \frac{3}{8} \cdot (x + 8)$

Step 4

Solve for $y$ .

Simplify $- \frac{3}{8} \cdot (x + 8)$ .

Rewrite.

$y - 1 = 0 + 0 - \frac{3}{8} \cdot (x + 8)$

Simplify terms.

Apply the distributive property.

$y - 1 = - \frac{3}{8} x - \frac{3}{8} \cdot 8$

Combine $x$ and $\frac{3}{8}$ .

$y - 1 = - \frac{x \cdot 3}{8} - \frac{3}{8} \cdot 8$

Cancel the common factor of $8$ .

Move the leading negative in $- \frac{3}{8}$ into the numerator.

$y - 1 = - \frac{x \cdot 3}{8} + \frac{- 3}{8} \cdot 8$

Cancel the common factor.

$y - 1 = - \frac{x \cdot 3}{8} + \frac{- 3}{8} \cdot 8$

Rewrite the expression.

$y - 1 = - \frac{x \cdot 3}{8} - 3$

Move $3$ to the left of $x$ .

$y - 1 = - \frac{3 x}{8} - 3$

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

Add $1$ to both sides of the equation.

$y = - \frac{3 x}{8} - 3 + 1$

Add $- 3$ and $1$ .

$y = - \frac{3 x}{8} - 2$

Step 5

Reorder terms.

$y = - (\frac{3}{8} x) - 2$

Step 6

Remove parentheses.

$y = - \frac{3}{8} x - 2$

Step 7

List the equation in different forms.

Slope-intercept form:

$y = - \frac{3}{8} x - 2$

Point-slope form:

$y - 1 = - \frac{3}{8} \cdot (x + 8)$

Step 8

Find the Equation Using Point-Slope Formula (-8,1) , (0,-2)

Related Questions

Support LCMGCF.com by disabling your adblocker.