Find the Equation Using Point-Slope Formula (0,0) , (6,2)

$(0, 0)$ , $(6, 2)$

Step 1

Find the slope of the line between $(0, 0)$ and $(6, 2)$ 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.

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

Simplify.

Simplify the numerator.

Multiply $- 1$ by $0$ .

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

Add $2$ and $0$ .

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

Simplify the denominator.

Multiply $- 1$ by $0$ .

$m = \frac{2}{6 + 0}$

Add $6$ and $0$ .

$m = \frac{2}{6}$

Cancel the common factor of $2$ and $6$ .

Factor $2$ out of $2$ .

$m = \frac{2 (1)}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

$m = \frac{1}{3}$

Step 2

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

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

Step 3

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

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

Step 4

Solve for $y$ .

Add $y$ and $0$ .

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

Simplify $\frac{1}{3} \cdot (x + 0)$ .

Add $x$ and $0$ .

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

Combine $\frac{1}{3}$ and $x$ .

$y = \frac{x}{3}$

Step 5

Reorder terms.

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

Step 6

List the equation in different forms.

Slope-intercept form:

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

Point-slope form:

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

Step 7

Find the Equation Using Point-Slope Formula (0,0) , (6,2)

Related Questions

Support LCMGCF.com by disabling your adblocker.