Question

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

y is wrong

Answer 2

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 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.