To find the slope and y-intercept of the equation \(9 + \frac{27}{2}x = -\frac{3}{2}y\), we first need to rearrange it into the slope-intercept form \(y = mx + b\), 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, let's isolate \(y\) on one side. We can start by multiplying both sides by \(-\frac{2}{3}\) to get \(y\) by itself:
\[ y = -\frac{2}{3}(9 + \frac{27}{2}x) \]
Distributing \(-\frac{2}{3}\):
\[ y = -\frac{2}{3} \cdot 9 - \frac{2}{3} \cdot \frac{27}{2}x \]
\[ y = -6 - 9x \]
Now we have the equation in the slope-intercept form:
\[ y = -9x - 6 \]
From this equation:
- The slope \(m\) is \(-9\).
- The y-intercept \(b\) is \(-6\).
The y-intercept as an ordered pair can be found by substituting \(x=0\):
\[ y = -6 \quad \text{when} \quad x = 0 \Rightarrow (0, -6) \]
Thus, the slope is \(-9\) and the y-intercept as an ordered pair is \((0, -6)\).