Find the Equation with a Point and Slope What is the equation of the line that passes through the point (-6,6) and has a slope of 1/3 ?

What is the equation of the line that passes through the point $(- 6, 6)$ and has a slope of $\frac{1}{3}$ ?

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.

$y = (\frac{1}{3}) \cdot (- 6) + b$

Substitute the value of $y$ into the equation.

$6 = (\frac{1}{3}) \cdot (- 6) + b$

Find the value of $b$ .

Rewrite the equation as $\frac{1}{3} \cdot - 6 + b = 6$ .

$\frac{1}{3} \cdot - 6 + b = 6$

Cancel the common factor of $3$ .

Factor $3$ out of $- 6$ .

$\frac{1}{3} \cdot (3 (- 2)) + b = 6$

Cancel the common factor.

$\frac{1}{3} \cdot (3 \cdot - 2) + b = 6$

Rewrite the expression.

$- 2 + b = 6$

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

Add $2$ to both sides of the equation.

$b = 6 + 2$

Add $6$ and $2$ .

$b = 8$

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.

$y = \frac{1}{3} x + 8$

Step 3