Question

What is the slope and the y -intercept of equation 9+27/2x=−3/2y . 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 will first rewrite it in slope-intercept form, which is \(y = mx + b\) where \(m\) is the slope and \(b\) is the y-intercept.

Starting with the given equation:

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

We can first isolate \(y\) by multiplying both sides by \(-\frac{2}{3}\):

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

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

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

Calculating the constant term:

\[
-\frac{2}{3} \cdot 9 = -6
\]

Calculating the coefficient of \(x\):

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

So, combining these, we find:

\[
y = -9x - 6
\]

Now, we can identify the slope and the y-intercept:

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

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

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