Question

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

Answer 1

wrong

Answer 2

To find the slope and y-intercept of the equation \( 9 + \frac{27}{2}x = -\frac{3}{2}y \), 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:

\[
9 + \frac{27}{2}x = -\frac{3}{2}y
\]

we can isolate \( y \) by first moving everything else to the other side:

\[
-\frac{3}{2}y = -\left(9 + \frac{27}{2}x\right)
\]

Now distribute the negative sign:

\[
-\frac{3}{2}y = -9 - \frac{27}{2}x
\]

Next, we can multiply both sides by -1 to make \( y \) positive:

\[
\frac{3}{2}y = 9 + \frac{27}{2}x
\]

Now, divide both sides by \(\frac{3}{2}\) or multiply by the reciprocal \(\frac{2}{3}\):

\[
y = \frac{2}{3} \cdot 9 + \frac{2}{3} \cdot \frac{27}{2}x
\]

Calculating each term separately:

\[
y = 6 + 9x
\]

Now, we rewrite it in the standard form of \( y = mx + b \):

\[
y = 9x + 6
\]

From this, we can see that:

- The slope \( m \) is \( 9 \).
- The y-intercept \( b \) is \( 6 \).

The y-intercept as an ordered pair is:

\[
(0, 6)
\]

In summary:
- The slope is \( 9 \)
- The y-intercept is \( (0, 6) \)

Answer 3

I apologize for any mistakes in my previous response. Let's carefully go through the problem step by step to find the correct slope and y-intercept for the equation \( 9 + \frac{27}{2}x = -\frac{3}{2}y \).

### Step 1: Rearranging the Equation

We start with the equation:

\[
9 + \frac{27}{2}x = -\frac{3}{2}y
\]

We want to solve for \( y \). First, isolate the term involving \( y \):

\[
-\frac{3}{2}y = -\left(9 + \frac{27}{2}x\right)
\]

This simplifies to:

\[
-\frac{3}{2}y = -9 - \frac{27}{2}x
\]

Now, multiplying through by -1 gives us:

\[
\frac{3}{2}y = 9 + \frac{27}{2}x
\]

### Step 2: Isolating \( y \)

Next, we need to solve for \( y \) by multiplying both sides by \( \frac{2}{3} \):

\[
y = \frac{2}{3}(9 + \frac{27}{2}x)
\]

Distributing \( \frac{2}{3} \) gives:

\[
y = \frac{2}{3} \cdot 9 + \frac{2}{3} \cdot \frac{27}{2}x
\]

Calculating each term:

1. \( \frac{2}{3} \cdot 9 = 6 \)
2. \( \frac{2}{3} \cdot \frac{27}{2} = 9 \)

Putting it all together:

\[
y = 9x + 6
\]

### Step 3: Identifying the Slope and Y-Intercept

From the equation \( y = 9x + 6 \):

- The slope \( m \) is \( 9 \).
- The y-intercept \( b \) is \( 6 \).

### Final Answer

The slope is \( 9 \) and the y-intercept is:

\[
(0, 6)
\]

If there are any specific issues or misunderstandings in the previous message, please let me know, and I'll be glad to correct them!