Find the Equation Using Point-Slope Formula (5,0) , (0,-6)

$(5, 0)$ , $(0, - 6)$

Step 1

Find the slope of the line between $(5, 0)$ and $(0, - 6)$ 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.

$m = \frac{- 6 - (0)}{0 - (5)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $0$ .

$m = \frac{- 6 + 0}{0 - (5)}$

Add $- 6$ and $0$ .

$m = \frac{- 6}{0 - (5)}$

Simplify the denominator.

Multiply $- 1$ by $5$ .

$m = \frac{- 6}{0 - 5}$

Subtract $5$ from $0$ .

$m = \frac{- 6}{- 5}$

Dividing two negative values results in a positive value.

$m = \frac{6}{5}$

Step 2

Use the slope $\frac{6}{5}$ and a given point $(5, 0)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (0) = \frac{6}{5} \cdot (x - (5))$

Step 3

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

$y + 0 = \frac{6}{5} \cdot (x - 5)$

Step 4

Solve for $y$ .

Add $y$ and $0$ .

$y = \frac{6}{5} \cdot (x - 5)$

Simplify $\frac{6}{5} \cdot (x - 5)$ .

Apply the distributive property.

$y = \frac{6}{5} x + \frac{6}{5} \cdot - 5$

Combine $\frac{6}{5}$ and $x$ .

$y = \frac{6 x}{5} + \frac{6}{5} \cdot - 5$

Cancel the common factor of $5$ .

Factor $5$ out of $- 5$ .

$y = \frac{6 x}{5} + \frac{6}{5} \cdot (5 (- 1))$

Cancel the common factor.

$y = \frac{6 x}{5} + \frac{6}{5} \cdot (5 \cdot - 1)$

Rewrite the expression.

$y = \frac{6 x}{5} + 6 \cdot - 1$

Multiply $6$ by $- 1$ .

$y = \frac{6 x}{5} - 6$

Step 5

Reorder terms.

$y = \frac{6}{5} x - 6$

Step 6

List the equation in different forms.

Slope-intercept form:

$y = \frac{6}{5} x - 6$

Point-slope form:

$y + 0 = \frac{6}{5} \cdot (x - 5)$

Step 7

Find the Equation Using Point-Slope Formula (5,0) , (0,-6)

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