What are the slope and the y-intercept of the equation 9+27/2 x=−3/2 y? Write the y-intercept as an ordered pair. (1 point)

Answer 1

To find the slope and the y-intercept of the equation \( 9 + \frac{27}{2}x = -\frac{3}{2}y \), we first need to rearrange this equation into the slope-intercept form, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

1. Start by isolating \( y \): \[ 9 + \frac{27}{2}x = -\frac{3}{2}y \]

2. To move \( -\frac{3}{2}y \) to the left side, we'll multiply both sides by \(-1\) to make the \( y \) term positive: \[ -9 - \frac{27}{2}x = \frac{3}{2}y \]

3. Now, we can solve for \( y \) by multiplying both sides by \( \frac{2}{3} \) to isolate \( y \): \[ y = -\frac{2}{3}(-9) - \frac{2}{3}\left(\frac{27}{2}x\right) \]

4. Simplifying this: \[ y = 6 - 9x \]

Now we have the equation in the form \( y = mx + b \):

• The slope \( m = -9 \)
• The y-intercept \( b = 6 \)

The y-intercept can be represented as an ordered pair \( (0, b) \):

• Y-intercept: \( (0, 6) \)

Thus, the final answers are:

• Slope: \( -9 \)
• Y-intercept: \( (0, 6) \)

Answer 2

y is wrong

Answer 3

Let's go through the steps to rewrite the equation \( 9 + \frac{27}{2}x = -\frac{3}{2}y \) into slope-intercept form more carefully.

1. Start with the original equation: \[ 9 + \frac{27}{2}x = -\frac{3}{2}y \]

2. First, isolate the \( y \) term by moving everything else to the other side: \[ -\frac{3}{2}y = 9 + \frac{27}{2}x \]

3. Next, multiply both sides by \( -\frac{2}{3} \) to solve for \( y \): \[ y = -\frac{2}{3}(9 + \frac{27}{2}x) \]

4. Distributing \( -\frac{2}{3} \): \[ y = -\frac{2}{3} \cdot 9 - \frac{2}{3} \cdot \frac{27}{2}x \]

   Simplifying:

   • The first term gives: \[ -\frac{2 \cdot 9}{3} = -6 \]
   • The second term simplifies to: \[ -\frac{27}{3}x = -9x \]

5. Putting it all together: \[ y = -9x - 6 \]

Now we have identified:

• The slope \( m = -9 \)
• The y-intercept \( b = -6 \)

The y-intercept as an ordered pair:

• \( (0, -6) \)

Final Answers

• Slope: \( -9 \)
• Y-intercept: \( (0, -6) \)

I apologize for the earlier mistake, and I appreciate your patience.