To find the slope and y-intercept of the equation \( 9 + 272x = -32y \), 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 the equation:
\[ 9 + 272x = -32y \]
We can isolate \( y \) by performing the following steps:
- Move \( 9 + 272x \) to the right side:
\[ -32y = -9 - 272x \]
- Divide every term by \(-32\) to solve for \( y \):
\[ y = \frac{-9}{-32} + \frac{-272}{-32}x \]
Simplifying the terms gives:
\[ y = \frac{9}{32} + \frac{272}{32}x \]
- Simplify further the coefficient of \( x \):
\[ y = \frac{9}{32} + 8.5x \]
So, we have:
\[ y = 8.5x + \frac{9}{32} \]
From this equation, we can identify the slope and y-intercept:
- Slope (\( m \)): \( 8.5 \)
- Y-intercept (\( b \)): \( \frac{9}{32} \)
The y-intercept as an ordered pair is \( (0, \frac{9}{32}) \).
Thus:
- The slope is \( 8.5 \).
- The y-intercept is \( (0, \frac{9}{32}) \).