Find the Equation Using Point-Slope Formula (-3,-6) ; m=-2/3

$(- 3, - 6)$ ; $m = - \frac{2}{3}$

Step 1

Use the slope $- \frac{2}{3}$ and a given point $(- 3, - 6)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 6) = - \frac{2}{3} \cdot (x - (- 3))$

Step 2

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

$y + 6 = - \frac{2}{3} \cdot (x + 3)$

Step 3

Solve for $y$ .

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

Rewrite.

$y + 6 = 0 + 0 - \frac{2}{3} \cdot (x + 3)$

Simplify terms.

Apply the distributive property.

$y + 6 = - \frac{2}{3} x - \frac{2}{3} \cdot 3$

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

$y + 6 = - \frac{x \cdot 2}{3} - \frac{2}{3} \cdot 3$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$y + 6 = - \frac{x \cdot 2}{3} + \frac{- 2}{3} \cdot 3$

Cancel the common factor.

$y + 6 = - \frac{x \cdot 2}{3} + \frac{- 2}{3} \cdot 3$

Rewrite the expression.

$y + 6 = - \frac{x \cdot 2}{3} - 2$

Move $2$ to the left of $x$ .

$y + 6 = - \frac{2 x}{3} - 2$

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

Subtract $6$ from both sides of the equation.

$y = - \frac{2 x}{3} - 2 - 6$

Subtract $6$ from $- 2$ .

$y = - \frac{2 x}{3} - 8$

Write in $y = m x + b$ form.

Reorder terms.

$y = - (\frac{2}{3} x) - 8$

Remove parentheses.

$y = - \frac{2}{3} x - 8$

Step 4

List the equation in different forms.

Slope-intercept form:

$y = - \frac{2}{3} x - 8$

Point-slope form:

$y + 6 = - \frac{2}{3} \cdot (x + 3)$

Step 5

Find the Equation Using Point-Slope Formula (-3,-6) ; m=-2/3

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