Find the Equation Using Slope-Intercept Form (3,-2) ; slope 1/3

$(3, - 2)$ ; slope $\frac{1}{3}$

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.

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

Substitute the value of $x$ into the equation.

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

Substitute the value of $y$ into the equation.

$- 2 = (\frac{1}{3}) \cdot (3) + b$

Find the value of $b$ .

Rewrite the equation as $\frac{1}{3} \cdot 3 + b = - 2$ .

$\frac{1}{3} \cdot 3 + b = - 2$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{1}{3} \cdot 3 + b = - 2$

Rewrite the expression.

$1 + b = - 2$

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

Subtract $1$ from both sides of the equation.

$b = - 2 - 1$

Subtract $1$ from $- 2$ .

$b = - 3$

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.

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