To find the slope and y-intercept of the equation \( 9 + \frac{27}{2}x = -\frac{3}{2}y \), we need to rewrite this equation 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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Let's isolate \( y \). First, rearranging gives: \[ -\frac{3}{2}y = -\frac{27}{2}x - 9 \]
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Now, to solve for \( y \), multiply both sides by \( -\frac{2}{3} \): \[ y = \frac{27}{3}x + 6 \]
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Simplifying this results in: \[ y = 9x + 6 \]
Now, we can identify the slope and the y-intercept.
- The slope \( m \) is \( 9 \).
- The y-intercept \( b \) is \( 6 \), which as an ordered pair is \( (0, 6) \).
Thus, the final answer is:
- The slope is \( 9 \).
- The y-intercept is \( (0, 6) \).