Find the Equation Using Point-Slope Formula (0,-3) , (2,1)

$(0, - 3)$ , $(2, 1)$

Step 1

Find the slope of the line between $(0, - 3)$ and $(2, 1)$ 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.

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

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 3$ .

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

Add $1$ and $3$ .

$m = \frac{4}{2 - (0)}$

Simplify the denominator.

Multiply $- 1$ by $0$ .

$m = \frac{4}{2 + 0}$

Add $2$ and $0$ .

$m = \frac{4}{2}$

Divide $4$ by $2$ .

$m = 2$

Step 2

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

$y - (- 3) = 2 \cdot (x - (0))$

Step 3

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

$y + 3 = 2 \cdot (x + 0)$

Step 4

Solve for $y$ .

Add $x$ and $0$ .

$y + 3 = 2 x$

Subtract $3$ from both sides of the equation.

$y = 2 x - 3$

Step 5

List the equation in different forms.

Slope-intercept form:

$y = 2 x - 3$

Point-slope form:

$y + 3 = 2 \cdot (x + 0)$

Step 6

Find the Equation Using Point-Slope Formula (0,-3) , (2,1)

Related Questions

Support LCMGCF.com by disabling your adblocker.