To find the slope and y-intercept of the equation \( 9 + \frac{27}{2}x = -\frac{3}{2}y \), we can rearrange the equation 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, isolate \( y \) on one side. We can multiply both sides by \(-\frac{2}{3}\) to move \( y \) to the left side:
\[ y = -\frac{2}{3}(9 + \frac{27}{2}x) \]
Distributing \(-\frac{2}{3}\):
\[ y = -\frac{2}{3} \times 9 - \frac{2}{3} \times \frac{27}{2}x \]
Calculating these:
\[ y = -6 - 9x \]
So the equation can be rewritten as:
\[ y = -9x - 6 \]
From the equation in slope-intercept form \( y = mx + b \):
- The slope \( m \) is \(-9\).
- The y-intercept \( b \) is \(-6\).
Thus, the slope is \(-9\) and the y-intercept is \(-6\).
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