Find the Equation Using Slope-Intercept Form (1,-5) ; slope -3/2

$(1, - 5)$ ; slope $- \frac{3}{2}$

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.

$y = (- \frac{3}{2}) \cdot (1) + b$

Substitute the value of $y$ into the equation.

$- 5 = (- \frac{3}{2}) \cdot (1) + b$

Find the value of $b$ .

Rewrite the equation as $- \frac{3}{2} \cdot 1 + b = - 5$ .

$- \frac{3}{2} \cdot 1 + b = - 5$

Multiply $- 1$ by $1$ .

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

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

Add $\frac{3}{2}$ to both sides of the equation.

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

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Combine $- 5$ and $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 5$ by $2$ .

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

Add $- 10$ and $3$ .

$b = \frac{- 7}{2}$

Move the negative in front of the fraction.

$b = - \frac{7}{2}$

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.

$y = - \frac{3}{2} x - \frac{7}{2}$