Find the Equation Using Slope-Intercept Form m=3/2 , (4,-9)

$m = \frac{3}{2}$ , $(4, - 9)$

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.

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

Substitute the value of $x$ into the equation.

$y = (\frac{3}{2}) \cdot (4) + b$

Substitute the value of $y$ into the equation.

$- 9 = (\frac{3}{2}) \cdot (4) + b$

Find the value of $b$ .

Rewrite the equation as $\frac{3}{2} \cdot 4 + b = - 9$ .

$\frac{3}{2} \cdot 4 + b = - 9$

Simplify each term.

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\frac{3}{2} \cdot (2 (2)) + b = - 9$

Cancel the common factor.

$\frac{3}{2} \cdot (2 \cdot 2) + b = - 9$

Rewrite the expression.

$3 \cdot 2 + b = - 9$

Multiply $3$ by $2$ .

$6 + b = - 9$

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

Subtract $6$ from both sides of the equation.

$b = - 9 - 6$

Subtract $6$ from $- 9$ .

$b = - 15$

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.

$y = \frac{3}{2} x - 15$

Step 3