To manipulate the equation \(9 + \frac{27}{2}x = -\frac{3}{2}y\), you can express \(y\) in terms of \(x\) or vice versa. Here’s how to isolate \(y\):
-
Start with the original equation:
\[ 9 + \frac{27}{2}x = -\frac{3}{2}y \]
-
Rearrange the equation to solve for \(y\):
\[ -\frac{3}{2}y = 9 + \frac{27}{2}x \]
-
Multiply both sides by \(-\frac{2}{3}\) to isolate \(y\):
\[ y = -\frac{2}{3}(9 + \frac{27}{2}x) \]
-
Distributing \(-\frac{2}{3}\):
\[ y = -\frac{2}{3} \cdot 9 - \frac{2}{3} \cdot \frac{27}{2}x \]
\[ y = -6 - 9x \]
So, the equation in terms of \(y\) is:
\[ y = -6 - 9x \]
This equation shows \(y\) as a function of \(x\).