Question

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)
The slope is
. The y
-intercept is (
).

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 rearrange the equation into the slope-intercept form, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Starting from the original equation:

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

We can isolate \( y \) by first moving all terms involving \( y \) to one side and the other terms to the other side:

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

Now, we can multiply every term by -1 to simplify:

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

Next, we want to solve for \( y \) by multiplying everything 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 each term:

\[
y = 6 + 9x
\]

Now, we have the equation in the slope-intercept form \( y = mx + b \), where:

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

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

Thus, the final answers are:

The slope is \( 9 \). The y-intercept is \( (0, 6) \).