Question

From the given proportional relationship, which of the following points lie on the same line?

(3, 1)
(3, 5)
(3, 9)
(2, 10)

Answer 1

To determine which points lie on the same line in a proportional relationship, we can check if the points maintain a consistent ratio of y/x.

First, let's examine the points provided:

1. (3, 1)
- Ratio: \( \frac{1}{3} \)

2. (3, 5)
- Ratio: \( \frac{5}{3} \)

3. (3, 9)
- Ratio: \( \frac{9}{3} = 3 \)

4. (2, 10)
- Ratio: \( \frac{10}{2} = 5 \)

Now, we can see:

- For (3, 1), the ratio is \( \frac{1}{3} \)
- For (3, 5), the ratio is \( \frac{5}{3} \)
- For (3, 9), the ratio is \( 3 \)
- For (2, 10), the ratio is \( 5 \)

Since all the points with an x-coordinate of 3 have different ratios, they do not lie on the same line. The point (2, 10) also has a separate ratio.

Therefore, no points from the given set share the same proportional relationship, and hence, none of these points lie on the same line.