Find the Equation Using Slope-Intercept Form (3,-3) , m=-6/5

$(3, - 3)$ , $m = - \frac{6}{5}$

Find the value of $b$ using the formula for the equation of a line.

Use the formula for the equation of a line to find $b$ .

$y = m x + b$

Substitute the value of $m$ into the equation.

$y = (- \frac{6}{5}) \cdot x + b$

Substitute the value of $x$ into the equation.

$y = (- \frac{6}{5}) \cdot (3) + b$

Substitute the value of $y$ into the equation.

$- 3 = (- \frac{6}{5}) \cdot (3) + b$

Find the value of $b$ .

Rewrite the equation as $- \frac{6}{5} \cdot 3 + b = - 3$ .

$- \frac{6}{5} \cdot 3 + b = - 3$

Simplify each term.

Multiply $- \frac{6}{5} \cdot 3$ .

Multiply $3$ by $- 1$ .

$- 3 (\frac{6}{5}) + b = - 3$

Combine $- 3$ and $\frac{6}{5}$ .

$\frac{- 3 \cdot 6}{5} + b = - 3$

Multiply $- 3$ by $6$ .

$\frac{- 18}{5} + b = - 3$

Move the negative in front of the fraction.

$- \frac{18}{5} + b = - 3$

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

Add $\frac{18}{5}$ to both sides of the equation.

$b = - 3 + \frac{18}{5}$

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$b = - 3 \cdot \frac{5}{5} + \frac{18}{5}$

Combine $- 3$ and $\frac{5}{5}$ .

$b = \frac{- 3 \cdot 5}{5} + \frac{18}{5}$

Combine the numerators over the common denominator.

$b = \frac{- 3 \cdot 5 + 18}{5}$

Simplify the numerator.

Multiply $- 3$ by $5$ .

$b = \frac{- 15 + 18}{5}$

Add $- 15$ and $18$ .

$b = \frac{3}{5}$

Now that the values of $m$ (slope) and $b$ (y-intercept) are known, substitute them into $y = m x + b$ to find the equation of the line.

$y = - \frac{6}{5} x + \frac{3}{5}$