Find the Equation Using Point-Slope Formula (-5,8) , (5,0)

$(- 5, 8)$ , $(5, 0)$

Step 1

Find the slope of the line between $(- 5, 8)$ and $(5, 0)$ 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.

$m = \frac{0 - (8)}{5 - (- 5)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $8$ .

$m = \frac{0 - 8}{5 - (- 5)}$

Subtract $8$ from $0$ .

$m = \frac{- 8}{5 - (- 5)}$

Simplify the denominator.

Multiply $- 1$ by $- 5$ .

$m = \frac{- 8}{5 + 5}$

Add $5$ and $5$ .

$m = \frac{- 8}{10}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $- 8$ and $10$ .

Factor $2$ out of $- 8$ .

$m = \frac{2 (- 4)}{10}$

Cancel the common factors.

Factor $2$ out of $10$ .

$m = \frac{2 \cdot - 4}{2 \cdot 5}$

Cancel the common factor.

$m = \frac{2 \cdot - 4}{2 \cdot 5}$

Rewrite the expression.

$m = \frac{- 4}{5}$

Move the negative in front of the fraction.

$m = - \frac{4}{5}$

Step 2

Use the slope $- \frac{4}{5}$ and a given point $(- 5, 8)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (8) = - \frac{4}{5} \cdot (x - (- 5))$

Step 3

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

$y - 8 = - \frac{4}{5} \cdot (x + 5)$

Step 4

Solve for $y$ .

Simplify $- \frac{4}{5} \cdot (x + 5)$ .

Rewrite.

$y - 8 = 0 + 0 - \frac{4}{5} \cdot (x + 5)$

Simplify terms.

Apply the distributive property.

$y - 8 = - \frac{4}{5} x - \frac{4}{5} \cdot 5$

Combine $x$ and $\frac{4}{5}$ .

$y - 8 = - \frac{x \cdot 4}{5} - \frac{4}{5} \cdot 5$

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{4}{5}$ into the numerator.

$y - 8 = - \frac{x \cdot 4}{5} + \frac{- 4}{5} \cdot 5$

Cancel the common factor.

$y - 8 = - \frac{x \cdot 4}{5} + \frac{- 4}{5} \cdot 5$

Rewrite the expression.

$y - 8 = - \frac{x \cdot 4}{5} - 4$

Move $4$ to the left of $x$ .

$y - 8 = - \frac{4 x}{5} - 4$

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

Add $8$ to both sides of the equation.

$y = - \frac{4 x}{5} - 4 + 8$

Add $- 4$ and $8$ .

$y = - \frac{4 x}{5} + 4$

Step 5

Reorder terms.

$y = - (\frac{4}{5} x) + 4$

Step 6

Remove parentheses.

$y = - \frac{4}{5} x + 4$

Step 7

List the equation in different forms.

Slope-intercept form:

$y = - \frac{4}{5} x + 4$

Point-slope form:

$y - 8 = - \frac{4}{5} \cdot (x + 5)$

Step 8

Find the Equation Using Point-Slope Formula (-5,8) , (5,0)

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