To find the slope and the y-intercept of the equation \( 9 + \frac{27}{2}x = -\frac{3}{2}y \), we can first rearrange it 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 \( 9 + \frac{27}{2}x \) to the other side:
\[ -\frac{3}{2}y = - (9 + \frac{27}{2}x) \]
This simplifies to:
\[ -\frac{3}{2}y = -9 - \frac{27}{2}x \]
Next, we multiply the entire equation by \(-\frac{2}{3}\) to solve for \( y \):
\[ y = \left(-\frac{2}{3}\right)(-9) + \left(-\frac{2}{3}\right)\left(-\frac{27}{2}x\right) \]
Simplifying this gives:
\[ y = 6 + 9x \]
Now the equation is in the form \( y = mx + b \) where:
- The slope \( m = 9 \)
- The y-intercept \( b = 6 \)
The y-intercept as an ordered pair (where \( y \) is equal to \( b \) and \( x \) is \( 0 \)) is \( (0, 6) \).
Thus, the answers are:
The slope is 9. The y-intercept is (0, 6).
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