Write in y=mx+b Form y+6=-3/2(x-5)

$y + 6 = - \frac{3}{2} (x - 5)$

Step 1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 2

Rewrite in slope-intercept form.

Simplify the right side.

Simplify $- \frac{3}{2} (x - 5)$ .

Apply the distributive property.

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

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

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

Multiply $- \frac{3}{2} \cdot - 5$ .

Multiply $- 5$ by $- 1$ .

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

Combine $5$ and $\frac{3}{2}$ .

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

Multiply $5$ by $3$ .

$y + 6 = - \frac{x \cdot 3}{2} + \frac{15}{2}$

Move $3$ to the left of $x$ .

$y + 6 = - \frac{3 x}{2} + \frac{15}{2}$

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

Subtract $6$ from both sides of the equation.

$y = - \frac{3 x}{2} + \frac{15}{2} - 6$

To write $- 6$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = - \frac{3 x}{2} + \frac{15}{2} - 6 \cdot \frac{2}{2}$

Combine $- 6$ and $\frac{2}{2}$ .

$y = - \frac{3 x}{2} + \frac{15}{2} + \frac{- 6 \cdot 2}{2}$

Combine the numerators over the common denominator.

$y = - \frac{3 x}{2} + \frac{15 - 6 \cdot 2}{2}$

Simplify the numerator.

Multiply $- 6$ by $2$ .

$y = - \frac{3 x}{2} + \frac{15 - 12}{2}$

Subtract $12$ from $15$ .

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

Write in $y = m x + b$ form.

Reorder terms.

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

Remove parentheses.

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