To determine which table represents a direct proportion, we need to see if each $y$ value changes in a constant ratio relative to $x$. In a direct proportion, the ratio $\frac{y}{x}$ should remain constant.

Let's analyze each table:

1. Table A:

   • Ratios: $\frac{5}{2} = 2.5$, $\frac{10}{4} = 2.5$, $\frac{15}{6} = 2.5$, $\frac{20}{8} = 2.5$
   • The ratio $\frac{y}{x}$ is constant (2.5), indicating a direct proportion.

2. Table B:

   • Ratios: $\frac{3}{1} = 3$, $\frac{6}{2} = 3$, $\frac{9}{3} = 3$, $\frac{14}{4} = 3.5$
   • The ratio changes from 3 to 3.5, indicating it’s not a direct proportion.

3. Table C:

   • Ratios: $\frac{4}{1} = 4$, $\frac{7}{2} = 3.5$, $\frac{10}{3} \approx 3.33$, $\frac{13}{4} = 3.25$
   • The ratio is not constant, so this is not a direct proportion.

4. Table D:

   • Ratios: $\frac{2}{1} = 2$, $\frac{6}{3} = 2$, $\frac{10}{5} = 2$, $\frac{14}{7} = 2$
   • The ratio $\frac{y}{x}$ is constant (2), indicating a direct proportion.

Conclusion:

Tables A and D represent direct proportions because their $\frac{y}{x}$ ratios remain constant.

Would you like further details or explanations?

Follow-up Questions

1. What are other examples of direct proportions in real life?
2. How can direct proportion be represented as an equation?
3. How do you identify an inverse proportion?
4. What happens to the value of $y$ as $x$ increases in direct proportion?
5. Can a graph represent a direct proportion? If so, how?

Tip

For direct proportions, the graph of $y$ vs. $x$ will always be a straight line passing through the origin.