To find the slope and the y-intercept of the equation \( 9 + \frac{27}{2}x = -\frac{3}{2}y \), we first need to rewrite it in the slope-intercept form, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
Let's start by isolating \( y \):
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Move the term involving \( x \) to the other side: \[ -\frac{3}{2}y = -9 - \frac{27}{2}x \]
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Now, multiply the entire equation by \(-\frac{2}{3}\) to solve for \( y \): \[ y = \frac{2}{3}(9 + \frac{27}{2}x) \]
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This further simplifies to: \[ y = -\frac{27}{2} \cdot \frac{2}{3}x - 6 \]
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Breaking it down: \[ y = -9x - 6 \]
Now that we have the equation in the form \( y = mx + b \), we can identify the slope and the y-intercept:
- The slope (\( m \)) is \(-9\).
- The y-intercept (\( b \)) is \(-6\), which we can write as the ordered pair \((0, -6)\).
Thus, the answers are:
The slope is \(-9\). The y-intercept is \((0, -6)\).