The pattern in the data table shows that the value of \( y \) is directly proportional to the value of \( X \). Specifically, it appears that \( y \) is equal to \( \frac{5}{3} \) times \( X \).
To confirm this, we can look at the ratios of \( y \) to \( X \):
- For \( X = 6 \), \( y = 10 \) ⇒ \( \frac{y}{X} = \frac{10}{6} = \frac{5}{3} \)
- For \( X = 12 \), \( y = 20 \) ⇒ \( \frac{y}{X} = \frac{20}{12} = \frac{5}{3} \)
- For \( X = 24 \), \( y = 40 \) ⇒ \( \frac{y}{X} = \frac{40}{24} = \frac{5}{3} \)
- For \( X = 48 \), \( y = 80 \) ⇒ \( \frac{y}{X} = \frac{80}{48} = \frac{5}{3} \)
Thus, the relationship can be expressed mathematically as:
\[ y = \frac{5}{3} X \]
This means that for every unit increase in \( X \), \( y \) increases by \( \frac{5}{3} \) units.
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