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, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
Starting with:
\[ 9 + \frac{27}{2}x = -\frac{3}{2}y \]
we can isolate \( y \) by first moving everything else to the other side:
\[ -\frac{3}{2}y = -\left(9 + \frac{27}{2}x\right) \]
Now distribute the negative sign:
\[ -\frac{3}{2}y = -9 - \frac{27}{2}x \]
Next, we can multiply both sides by -1 to make \( y \) positive:
\[ \frac{3}{2}y = 9 + \frac{27}{2}x \]
Now, divide both sides by \(\frac{3}{2}\) or multiply by the reciprocal \(\frac{2}{3}\):
\[ y = \frac{2}{3} \cdot 9 + \frac{2}{3} \cdot \frac{27}{2}x \]
Calculating each term separately:
\[ y = 6 + 9x \]
Now, we rewrite it in the standard form of \( y = mx + b \):
\[ y = 9x + 6 \]
From this, we can see that:
- The slope \( m \) is \( 9 \).
- The y-intercept \( b \) is \( 6 \).
The y-intercept as an ordered pair is:
\[ (0, 6) \]
In summary:
- The slope is \( 9 \)
- The y-intercept is \( (0, 6) \)