Question

Is the table proportional or non-proportional?

X=-9,-8,-7,-6
Y=13.5,12,10.5,9

Answer 1

To determine whether the relationship between the two sets of values (X and Y) is proportional, we need to check if the ratio of Y to X remains constant across the values given.

The table provided has the following pairs:

- For \( X = -9 \), \( Y = 13.5 \)
- For \( X = -8 \), \( Y = 12 \)
- For \( X = -7 \), \( Y = 10.5 \)
- For \( X = -6 \), \( Y = 9 \)

We can calculate the ratios \( \frac{Y}{X} \) for each pair:

1. For \( X = -9 \), \( Y = 13.5 \):
\[
\frac{Y}{X} = \frac{13.5}{-9} = -1.5
\]

2. For \( X = -8 \), \( Y = 12 \):
\[
\frac{Y}{X} = \frac{12}{-8} = -1.5
\]

3. For \( X = -7 \), \( Y = 10.5 \):
\[
\frac{Y}{X} = \frac{10.5}{-7} = -1.5
\]

4. For \( X = -6 \), \( Y = 9 \):
\[
\frac{Y}{X} = \frac{9}{-6} = -1.5
\]

Since the ratio \( \frac{Y}{X} \) is constant at \(-1.5\) for all pairs, we can conclude that the relationship between X and Y is proportional.