for which table(s) of values is the relationship linear and how?

Question

X 5 10 15 20 25 30
Y 20 30 40 50 50 50
I don't understand this at all...please help!!!

Answer 1

If y= k x + b, a linear relationship, lets increment it a bit.
changeiny= k*changeinX
Notice no matter what values x and y have, the changes are related by k.
Take the above data. Notice the first increment of x, 5 to 10, A change of 5. The change in y is 10 (20 to 30). The ratios of y/x is 2 (10/5). That ratio is x.Now try other places in the data.
Look at the end, x goes from 25 to 30, a change of 5. But y does not change (50 to 50). We would have expeced a change ratio of 2, or 2*5=10 if it were linear.
So the data is not a linear relationship.