To find the slope and the \( y \)-intercept of the equation \( 9 + \frac{27}{2}x = -\frac{3}{2}y \), we need to rearrange it into the slope-intercept form, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the \( y \)-intercept.
Starting with the given equation:
\[ 9 + \frac{27}{2}x = -\frac{3}{2}y \]
First, we can isolate \( y \) by multiplying through by \(-1\):
\[ -\left(9 + \frac{27}{2}x\right) = \frac{3}{2}y \]
This simplifies to:
\[ -\frac{27}{2}x - 9 = \frac{3}{2}y \]
Now, we can multiply everything by \(\frac{2}{3}\) to solve for \( y \):
\[ y = -\frac{27}{2} \cdot \frac{2}{3} x - 9 \cdot \frac{2}{3} \]
Calculating the coefficients gives:
\[ y = -\frac{27 \cdot 2}{2 \cdot 3} x - 6 = -\frac{27}{3} x - 6 = -9x - 6 \]
Now our equation in slope-intercept form is:
\[ y = -9x - 6 \]
From this, we can identify the slope \( m \) and the \( y \)-intercept \( b \):
- Slope \( m \): \(-9\)
- \( y \)-intercept \( b \): \(-6\)
The \( y \)-intercept as an ordered pair (where \( x = 0 \)) is:
\((0, -6)\)
Thus, the final answers are:
- Slope: \(-9\)
- \( y \)-intercept: \((0, -6)\)