Question

Determine which type of rule is represented in the table. What are the missing values?
x y
4 8
8 __
12 __

Answer 1

To determine the rule represented in the table, we can start by analyzing the given values for \( x \) and \( y \).

Given:
- When \( x = 4 \), \( y = 8 \).

We can see that when \( x \) increases by 4 (from 4 to 8), we need to determine the change in \( y \).

Let's assume a linear rule of the form \( y = kx \) where \( k \) is some constant. From the first value:
\[
y = 2x \quad \text{since } 8 = 2 \cdot 4
\]

Now, let's test this rule with the other \( x \) values:

1. For \( x = 8 \):
\[
y = 2 \cdot 8 = 16
\]

2. For \( x = 12 \):
\[
y = 2 \cdot 12 = 24
\]

Now we can summarize the completed table:

| \( x \) | \( y \) |
|---------|---------|
| 4 | 8 |
| 8 | 16 |
| 12 | 24 |

Thus, the missing values are:
- When \( x = 8 \), \( y = 16 \)
- When \( x = 12 \), \( y = 24 \)

The rule represented is \( y = 2x \).