Find the Equation with a Point and Slope What is the equation of the line that passes through the point (6,-3) and has a slope of -2/3 ?

What is the equation of the line that passes through the point $(6, - 3)$ and has a slope of $- \frac{2}{3}$ ?

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.

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

Substitute the value of $x$ into the equation.

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

Substitute the value of $y$ into the equation.

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

Find the value of $b$ .

Rewrite the equation as $- \frac{2}{3} \cdot 6 + b = - 3$ .

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

Simplify each term.

Cancel the common factor of $3$ .

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

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

Factor $3$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

$- 2 \cdot 2 + b = - 3$

Multiply $- 2$ by $2$ .

$- 4 + b = - 3$

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

Add $4$ to both sides of the equation.

$b = - 3 + 4$

Add $- 3$ and $4$ .

$b = 1$

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.

$y = - \frac{2}{3} x + 1$

Step 3