To determine whether $x$ and $y$ are proportional in each table, we need to check if there is a constant ratio between $y$ and $x$ for each pair of values. If $y = kx$ for some constant $k$, then $x$ and $y$ are proportional, and $k$ is the value that would go in the blank.

Let's examine each table individually.

Table 1

Values of $x$: 6, 8, 10
Values of $y$: 18, 48, 30

To find if there’s a constant $k$ where $y = kx$:

1. $\frac{y}{x} = \frac{18}{6} = 3$
2. $\frac{y}{x} = \frac{48}{8} = 6$
3. $\frac{y}{x} = \frac{30}{10} = 3$

Since the ratio between $y$ and $x$ is not consistent (it changes from 3 to 6), Table 1 is not proportional.

Table 2

Values of $x$: 6, 9, 12
Values of $y$: 12, 18, 24

To check if there’s a constant $k$ where $y = kx$:

1. $\frac{y}{x} = \frac{12}{6} = 2$
2. $\frac{y}{x} = \frac{18}{9} = 2$
3. $\frac{y}{x} = \frac{24}{12} = 2$

Since the ratio between $y$ and $x$ is consistent (always 2), Table 2 is proportional, and $y$ is $2$ times $x$.

Summary

• Table 1: Not proportional.
• Table 2: Proportional, with $y = 2 \times x$.

Would you like further details or have any questions?

1. How do you determine if two variables are proportional?
2. What are some real-life examples of proportional relationships?
3. How do you simplify ratios?
4. What is the significance of the constant of proportionality?
5. How do non-proportional relationships differ in graphs compared to proportional ones?

Tip: When checking for proportionality, always simplify the ratio $\frac{y}{x}$ to see if it remains consistent across all data points.