Data table

Question

X y
6. 10
12. 20
24. 40
48. 80
What is the pattern between the quantities in the table

Answer 1

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.