Given:
We get the points (5,1), (10, 2), (15,3), and (20, 4) from the table.
Required:
We need to check the relation of the given table.
Step-by-step explanation:
Recall that in a proportional relationship, one variable is always a constant value time the other.
The form of the proportional relationship is
![y=kx](https://img.qammunity.org/2023/formulas/mathematics/college/zfnjlk9kn7jg7cyy0nlnepmsiaxj3b2oge.png)
The values x=5 and y=1 can be written as follows.
![1=((1)/(5))\cdot5](https://img.qammunity.org/2023/formulas/mathematics/college/xbcm2sop4ji3enoxxylrrbqx49iyoqyw0g.png)
Here we get k=1/5.
The values x=10 and y=2 can be written as follows.
![2=((1)/(5))\cdot10](https://img.qammunity.org/2023/formulas/mathematics/college/at286cha9hn1lgabvz8szmb5cv2lg5fzjo.png)
Here we get k=1/5.
The values x=15 and y=3 can be written as follows.
![3=((1)/(5))\cdot15](https://img.qammunity.org/2023/formulas/mathematics/college/93igfpdbk75nf1a3fu25otjn9frszcuvhy.png)
Here we get k=1/5.
The values x=20 and y=4 can be written as follows.
![4=((1)/(5))\cdot20](https://img.qammunity.org/2023/formulas/mathematics/college/1am4r8y72y2gi29fwksci7vg4wbi9f1o19.png)
Here we get k=1/5.
There is a common constant k=1/5.
The table represents the proportional relationship.
Final answer:
The table represents the proportional relationship.