Question

What is the slope and 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 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 from the given equation:

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

We want to isolate \(y\). First, let's move \(-\frac{3}{2}y\) to the left side:

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

Now, multiply both sides by \(-\frac{2}{3}\) to solve for \(y\):

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

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

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

Calculating each term:

\[
y = -6 - 9x
\]

Now, we can see that this is in the form \(y = mx + b\) where:

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

The y-intercept as an ordered pair is \((0, -6)\).

So, the slope is \(-9\) and the y-intercept is \((0, -6)\).