Find the Equation Using Slope-Intercept Form (-2,-8) , m=1/3

$(- 2, - 8)$ , $m = \frac{1}{3}$

Step 1

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.

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

Substitute the value of $y$ into the equation.

$- 8 = (\frac{1}{3}) \cdot (- 2) + b$

Find the value of $b$ .

Rewrite the equation as $\frac{1}{3} \cdot - 2 + b = - 8$ .

$\frac{1}{3} \cdot - 2 + b = - 8$

Simplify each term.

Combine $\frac{1}{3}$ and $- 2$ .

$\frac{- 2}{3} + b = - 8$

Move the negative in front of the fraction.

$- \frac{2}{3} + b = - 8$

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

Add $\frac{2}{3}$ to both sides of the equation.

$b = - 8 + \frac{2}{3}$

To write $- 8$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$b = - 8 \cdot \frac{3}{3} + \frac{2}{3}$

Combine $- 8$ and $\frac{3}{3}$ .

$b = \frac{- 8 \cdot 3}{3} + \frac{2}{3}$

Combine the numerators over the common denominator.

$b = \frac{- 8 \cdot 3 + 2}{3}$

Simplify the numerator.

Multiply $- 8$ by $3$ .

$b = \frac{- 24 + 2}{3}$

Add $- 24$ and $2$ .

$b = \frac{- 22}{3}$

Move the negative in front of the fraction.

$b = - \frac{22}{3}$

Step 2

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.

$y = \frac{1}{3} x - \frac{22}{3}$

Step 3