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

Starting with the original equation:

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

First, we can isolate \( y \) by multiplying the entire equation by \(-\frac{2}{3}\) to eliminate the coefficient of \( y \):

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

Now let's simplify the left side:

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

Calculating each term:

\[
y = -6 - 9x
\]

This can be rewritten in the standard \( y = mx + b \) form:

\[
y = -9x - 6
\]

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

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

Finally, we express the y-intercept as an ordered pair. The y-intercept occurs at \( x = 0 \):

\[
(0, -6)
\]

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

**Final answer:**
The slope is \(-9\). The y-intercept is \((0, -6)\).