Find the Equation Using Point-Slope Formula (0,-4) , (6,0)

$(0, - 4)$ , $(6, 0)$

Step 1

Find the slope of the line between $(0, - 4)$ and $(6, 0)$ 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.

$m = \frac{0 - (- 4)}{6 - (0)}$

Simplify.

Cancel the common factor of $0 - (- 4)$ and $6 - (0)$ .

Rewrite $6$ as $- 1 (- 6)$ .

$m = \frac{0 - (- 4)}{- 1 \cdot - 6 - (0)}$

Factor $- 1$ out of $- 1 (- 6) - (0)$ .

$m = \frac{0 - (- 4)}{- 1 (- 6 + 0)}$

Reorder terms.

$m = \frac{0 - 4 \cdot - 1}{- 1 (- 6 + 0)}$

Factor $2$ out of $0$ .

$m = \frac{2 (0) - 4 \cdot - 1}{- 1 (- 6 + 0)}$

Factor $2$ out of $- 4 \cdot - 1$ .

$m = \frac{2 (0) + 2 (- 2 \cdot - 1)}{- 1 (- 6 + 0)}$

Factor $2$ out of $2 (0) + 2 (- 2 \cdot - 1)$ .

$m = \frac{2 (0 - 2 \cdot - 1)}{- 1 (- 6 + 0)}$

Cancel the common factors.

Factor $2$ out of $- 1 (- 6 + 0)$ .

$m = \frac{2 (0 - 2 \cdot - 1)}{2 (- 1 (- 3 + 0))}$

Cancel the common factor.

$m = \frac{2 (0 - 2 \cdot - 1)}{2 (- 1 (- 3 + 0))}$

Rewrite the expression.

$m = \frac{0 - 2 \cdot - 1}{- 1 (- 3 + 0)}$

Simplify the numerator.

Multiply $- 2$ by $- 1$ .

$m = \frac{0 + 2}{- 1 (- 3 + 0)}$

Add $0$ and $2$ .

$m = \frac{2}{- 1 (- 3 + 0)}$

Simplify the expression.

Add $- 3$ and $0$ .

$m = \frac{2}{- 1 \cdot - 3}$

Multiply $- 1$ by $- 3$ .

$m = \frac{2}{3}$

Step 2

Use the slope $\frac{2}{3}$ and a given point $(0, - 4)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 4) = \frac{2}{3} \cdot (x - (0))$

Step 3

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

$y + 4 = \frac{2}{3} \cdot (x + 0)$

Step 4

Solve for $y$ .

Simplify $\frac{2}{3} \cdot (x + 0)$ .

Add $x$ and $0$ .

$y + 4 = \frac{2}{3} \cdot x$

Combine $\frac{2}{3}$ and $x$ .

$y + 4 = \frac{2 x}{3}$

Subtract $4$ from both sides of the equation.

$y = \frac{2 x}{3} - 4$

Step 5

Reorder terms.

$y = \frac{2}{3} x - 4$

Step 6

List the equation in different forms.

Slope-intercept form:

$y = \frac{2}{3} x - 4$

Point-slope form:

$y + 4 = \frac{2}{3} \cdot (x + 0)$

Step 7

Find the Equation Using Point-Slope Formula (0,-4) , (6,0)

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