Question

9 - x = 3/2y
What are the points to plot

Answer 1

To plot the equation \( 9 - x = \frac{3}{2} y \), we can rearrange it to find \( y \) in terms of \( x \).

Starting with the original equation:

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

Rearranging gives:

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

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

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

Simplifying further:

\[
y = 6 - \frac{2}{3}x
\]

This is now in the slope-intercept form \( y = mx + b \), where the slope \( m = -\frac{2}{3} \) and the y-intercept \( b = 6 \).

### Points to Plot

To plot the line, we can calculate a few points by choosing some \( x \) values and finding the corresponding \( y \) values.

1. **When \( x = 0 \)**:
\[
y = 6 - \frac{2}{3}(0) = 6 \quad \Rightarrow \quad (0, 6)
\]

2. **When \( x = 3 \)**:
\[
y = 6 - \frac{2}{3}(3) = 6 - 2 = 4 \quad \Rightarrow \quad (3, 4)
\]

3. **When \( x = 6 \)**:
\[
y = 6 - \frac{2}{3}(6) = 6 - 4 = 2 \quad \Rightarrow \quad (6, 2)
\]

4. **When \( x = 9 \)**:
\[
y = 6 - \frac{2}{3}(9) = 6 - 6 = 0 \quad \Rightarrow \quad (9, 0)
\]

5. **When \( x = 12 \)**:
\[
y = 6 - \frac{2}{3}(12) = 6 - 8 = -2 \quad \Rightarrow \quad (12, -2)
\]

### Points Summary

The points to plot are:

- \( (0, 6) \)
- \( (3, 4) \)
- \( (6, 2) \)
- \( (9, 0) \)
- \( (12, -2) \)

You can plot these points on a graph and draw a line through them to represent the equation \( 9 - x = \frac{3}{2} y \).