Find the Equation with a Point and Slope What is the equation of the line that passes through the point (6,-5) and has a slope of -3/2 ?

What is the equation of the line that passes through the point $(6, - 5)$ and has a slope of $- \frac{3}{2}$ ?

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.

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

Substitute the value of $x$ into the equation.

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

Substitute the value of $y$ into the equation.

$- 5 = (- \frac{3}{2}) \cdot (6) + b$

Find the value of $b$ .

Rewrite the equation as $- \frac{3}{2} \cdot 6 + b = - 5$ .

$- \frac{3}{2} \cdot 6 + b = - 5$

Simplify each term.

Cancel the common factor of $2$ .

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

$\frac{- 3}{2} \cdot 6 + b = - 5$

Factor $2$ out of $6$ .

$\frac{- 3}{2} \cdot (2 (3)) + b = - 5$

Cancel the common factor.

$\frac{- 3}{2} \cdot (2 \cdot 3) + b = - 5$

Rewrite the expression.

$- 3 \cdot 3 + b = - 5$

Multiply $- 3$ by $3$ .

$- 9 + b = - 5$

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

Add $9$ to both sides of the equation.

$b = - 5 + 9$

Add $- 5$ and $9$ .

$b = 4$

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.

$y = - \frac{3}{2} x + 4$