To find the slope and the y-intercept of the equation \( 9 + \frac{27}{2}x = -\frac{3}{2}y \), we need to 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 original equation:
\[ 9 + \frac{27}{2}x = -\frac{3}{2}y \]
First, we can isolate \( y \) by multiplying the entire equation by \(-\frac{2}{3}\) to eliminate the coefficient of \( y \):
\[ -\frac{2}{3}(9 + \frac{27}{2}x) = y \]
Now let's simplify the left side:
\[ y = -\frac{2}{3} \cdot 9 - \frac{2}{3} \cdot \frac{27}{2}x \]
Calculating each term:
\[ y = -6 - 9x \]
This can be rewritten in the standard \( y = mx + b \) form:
\[ y = -9x - 6 \]
From this equation, we can identify the slope \( m \) and the y-intercept \( b \):
- The slope \( m \) is \(-9\).
- The y-intercept \( b \) is \(-6\).
Finally, we express the y-intercept as an ordered pair. The y-intercept occurs at \( x = 0 \):
\[ (0, -6) \]
Therefore, the slope is \(-9\) and the y-intercept is \((0, -6)\).
Final answer: The slope is \(-9\). The y-intercept is \((0, -6)\).
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