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

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

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.

$y = (- 3) \cdot x + b$

Substitute the value of $x$ into the equation.

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

Substitute the value of $y$ into the equation.

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

Find the value of $b$ .

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

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

Simplify each term.

Multiply $- 3 (\frac{3}{2})$ .

Combine $- 3$ and $\frac{3}{2}$ .

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

Multiply $- 3$ by $3$ .

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

Move the negative in front of the fraction.

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

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

Add $\frac{9}{2}$ to both sides of the equation.

$b = 3 + \frac{9}{2}$

To write $3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Combine $3$ and $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $3$ by $2$ .

$b = \frac{6 + 9}{2}$

Add $6$ and $9$ .

$b = \frac{15}{2}$

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.

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

Step 3