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 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 \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

Starting with the given equation:

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

First, let's isolate \(y\) on one side. We can start by multiplying both sides by \(-\frac{2}{3}\) to get \(y\) by itself:

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

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

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

\[
y = -6 - 9x
\]

Now we have the equation in the slope-intercept form:

\[
y = -9x - 6
\]

From this equation:

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

The y-intercept as an ordered pair can be found by substituting \(x=0\):

\[
y = -6 \quad \text{when} \quad x = 0 \Rightarrow (0, -6)
\]

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