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.

Answer 1

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

Starting from the given equation:

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

We can isolate \(y\) by first eliminating the term on the left side. Subtract \(9 + \frac{27}{2}x\) from both sides:

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

Now, multiply through by \(-1\) to make \(y\) positive:

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

Now, we can rearrange this into the form \(y = mx + b\):

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

Next, divide everything by \(\frac{3}{2}\) to solve for \(y\):

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

Calculating each part:

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

Thus, we have:

\[
y = -6 - 9x
\]

Now, rearranging gives:

\[
y = -9x - 6
\]

From this equation, we can identify the slope \(m\) and the y-intercept \(b\):

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

To express the y-intercept as an ordered pair, we write it as \((0, -6)\).

### Final Answer:
- Slope: \(-9\)
- y-intercept: \((0, -6)\)