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 slope-intercept form, which is \( y = mx + b \) where \( m \) is the slope and \( b \) is the y-intercept.
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Start with the given equation: \[ 9 + \frac{27}{2}x = -\frac{3}{2}y \]
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Isolate \( y \) on one side. First, move the term involving \( x \) to the other side: \[ -\frac{3}{2}y = -\frac{27}{2}x - 9 \]
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Now, multiply everything by \(-\frac{2}{3}\) to solve for \( y \): \[ y = \frac{27}{3}x + 6 \]
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Simplify: \[ y = 9x + 6 \]
Now we can identify the slope and y-intercept from the equation:
- The slope \( m \) is 9.
- The y-intercept \( b \) is 6, which corresponds to the point \( (0, 6) \).
Therefore, the answers are:
- The slope is 9.
- The y-intercept is (0, 6).