Question

Which of the following tables represents a linear relationship that is also proportional?


x y
0 0
4 2
8 4

x y
0 1
2 3
4 5

x y
0 2
3 5
6 8

x y
0 3
6 5
12 7
Q

Answer 1

To determine which of the tables represents a linear relationship that is also proportional, we need to look for two criteria:

1. **Linear Relationship**: This means that the relationship can be expressed with the equation of a line (y = mx + b), where m is the slope and b is the y-intercept.
2. **Proportional Relationship**: This means that the relationship passes through the origin (0,0), which implies that the y-intercept (b) is zero. In other words, for every value of x, there should be a constant ratio of y/x.

Let's evaluate each table:

1. **Table 1:**
```
x y
0 0
4 2
8 4
```
- 0,0 indicates the relationship goes through the origin.
- The ratios are: \( \frac{2}{4} = 0.5 \) and \( \frac{4}{8} = 0.5 \) (constant).
- This is proportional and a linear relationship (y = 0.5x).

2. **Table 2:**
```
x y
0 1
2 3
4 5
```
- 0,1 does not indicate it goes through the origin.
- Not proportional (y-intercept is not zero).

3. **Table 3:**
```
x y
0 2
3 5
6 8
```
- 0,2 does not indicate it goes through the origin.
- Not proportional (y-intercept is not zero).

4. **Table 4:**
```
x y
0 3
6 5
12 7
```
- 0,3 does not indicate it goes through the origin.
- Not proportional (y-intercept is not zero).

**Conclusion:** The first table (Table 1) is the only one that represents a linear relationship that is also proportional.