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

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

Step 1

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

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

Simplify.

Simplify the numerator.

Multiply $- 1$ by $3$ .

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

Subtract $3$ from $- 1$ .

$m = \frac{- 4}{0 - (- 3)}$

Simplify the denominator.

Multiply $- 1$ by $- 3$ .

$m = \frac{- 4}{0 + 3}$

Add $0$ and $3$ .

$m = \frac{- 4}{3}$

Move the negative in front of the fraction.

$m = - \frac{4}{3}$

Step 2

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

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

Step 3

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

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

Step 4

Solve for $y$ .

Simplify $- \frac{4}{3} \cdot (x + 3)$ .

Rewrite.

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

Simplify terms.

Apply the distributive property.

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

Combine $x$ and $\frac{4}{3}$ .

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

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{4}{3}$ into the numerator.

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

Add $3$ to both sides of the equation.

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

Add $- 4$ and $3$ .

$y = - \frac{4 x}{3} - 1$

Step 5

Reorder terms.

$y = - (\frac{4}{3} x) - 1$

Step 6

Remove parentheses.

$y = - \frac{4}{3} x - 1$

Step 7

List the equation in different forms.

Slope-intercept form:

$y = - \frac{4}{3} x - 1$

Point-slope form:

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

Step 8

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

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