Find the Equation with a Point and Slope (10,-3) , -3/2

$(10, - 3)$ , $- \frac{3}{2}$

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.

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

Substitute the value of $x$ into the equation.

$y = (- \frac{3}{2}) \cdot (10) + b$

Substitute the value of $y$ into the equation.

$- 3 = (- \frac{3}{2}) \cdot (10) + b$

Find the value of $b$ .

Rewrite the equation as $- \frac{3}{2} \cdot 10 + b = - 3$ .

$- \frac{3}{2} \cdot 10 + b = - 3$

Simplify each term.

Cancel the common factor of $2$ .

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

$\frac{- 3}{2} \cdot 10 + b = - 3$

Factor $2$ out of $10$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $- 3$ by $5$ .

$- 15 + b = - 3$

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

Add $15$ to both sides of the equation.

$b = - 3 + 15$

Add $- 3$ and $15$ .

$b = 12$

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.

$y = - \frac{3}{2} x + 12$

Step 3