for which table(s) of values is the relationship linear and how?
X 5 10 15 20 25 30
Y 20 30 40 50 50 50
I don't understand this at all...please help!!!
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.
To determine if a relationship between two variables is linear, we need to check if the ratio between the change in the dependent variable (Y) and the change in the independent variable (X) is constant.
Let's calculate the differences between consecutive values of X and Y:
For X:
- The difference between 10 and 5 is 5.
- The difference between 15 and 10 is 5.
- The difference between 20 and 15 is 5.
- The difference between 25 and 20 is 5.
- The difference between 30 and 25 is 5.
For Y:
- The difference between 30 and 20 is 10.
- The difference between 40 and 30 is 10.
- The difference between 50 and 40 is 10.
- The difference between 50 and 50 is 0.
- The difference between 50 and 50 is 0.
As you can see, the differences between consecutive values of X are constant (5), while the differences between consecutive values of Y are not constant. The differences for Y are 10, 10, 0, and 0, which means they are not constant.
Therefore, based on the given table of values, the relationship between X and Y is not linear.