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What is the slope and the y -intercept of the equation 9+272x=−32y . Write the y -intercept as an ordered pair.(1 point) The slope is . The y -intercept is (). Remaining Attempts : 3

3 answers

To find the slope and the y-intercept of the equation \( 9 + 272x = -32y \), we need to rearrange it into the slope-intercept form (\( y = mx + b \)), where \( m \) is the slope and \( b \) is the y-intercept.

Starting with the equation:

\[ 9 + 272x = -32y \]

First, we isolate \( y \) by moving the term involving \( 9 \) and \( 272x \) to the other side:

\[ -32y = -272x - 9 \]

Next, divide all terms by \(-32\):

\[ y = \frac{272}{32}x + \frac{9}{32} \]

Now simplify \(\frac{272}{32}\):

\[ y = 8.5x + \frac{9}{32} \]

So now we see that the slope \( m \) is \( 8.5 \), and the y-intercept \( b \) is \(\frac{9}{32}\).

The y-intercept as an ordered pair is \( (0, \frac{9}{32}) \).

Therefore:

  • The slope is \( 8.5 \).
  • The y-intercept is \( (0, \frac{9}{32}) \).
nope

Apologies for the confusion. Let's carefully work through the equation again step by step to find the slope and y-intercept accurately.

Starting with the equation:

\[ 9 + 272x = -32y \]

Our goal is to solve for \( y \):

  1. Move \( 9 + 272x \) to the right side:

\[ -32y = -272x - 9 \]

  1. Then, divide every term by \(-32\) to solve for \( y \):

\[ y = \frac{272}{32}x + \frac{9}{32} \]

  1. Simplify \(\frac{272}{32}\):

\[ \frac{272}{32} = 8.5 \]

So the equation becomes:

\[ y = -8.5x - \frac{9}{32} \]

Now we can find the slope and y-intercept:

  • The slope \( m \) is \(-8.5\).
  • The y-intercept \( b \) (the constant term when \( y \) is in terms of \( x \)) is \(-\frac{9}{32}\).

As an ordered pair, the y-intercept is:

\[ \left(0, -\frac{9}{32}\right) \]

Summary:

  • The slope is \(-8.5\).
  • The y-intercept is \(\left(0, -\frac{9}{32}\right)\).

If there's a specific part you believe is incorrect, please let me know!