To find the slope and the y-intercept of the equation \( 9 + \frac{27}{2}x = -\frac{3}{2}y \), we will first rearrange the equation into the slope-intercept form, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
Starting from the original equation:
\[ 9 + \frac{27}{2}x = -\frac{3}{2}y \]
We can isolate \( y \) by first moving all terms involving \( y \) to one side and the other terms to the other side:
\[ -\frac{3}{2}y = -9 - \frac{27}{2}x \]
Now, we can multiply every term by -1 to simplify:
\[ \frac{3}{2}y = 9 + \frac{27}{2}x \]
Next, we want to solve for \( y \) by multiplying everything by \( \frac{2}{3} \):
\[ y = \frac{2}{3}(9 + \frac{27}{2}x) \]
Distributing \( \frac{2}{3} \):
\[ y = \frac{2}{3} \cdot 9 + \frac{2}{3} \cdot \frac{27}{2}x \]
Calculating each term:
\[ y = 6 + 9x \]
Now, we have the equation in the slope-intercept form \( y = mx + b \), where:
- The slope \( m \) is \( 9 \)
- The y-intercept \( b \) is \( 6 \)
The y-intercept as an ordered pair is \( (0, 6) \).
Thus, the final answers are:
The slope is \( 9 \). The y-intercept is \( (0, 6) \).