For which table(s) of values in Exercises 39–42 is the relationship
linear? Tell how you decided. Write the equation for each linear
relationship.
x y
5 20
10 30
15 40
20 50
25 50
30 50
bobpursley stated "Look at y. It stays constant at the end. If it were always constant, it would be linear...a horizontal line with zero slope. But near the origin, it is not constant.
The relation is not linear."
My question then is: "So, no part of the table is linear? I mean, the x=5, y=20; x=10, y=30; & x=15, y=40, none of those are linear either? Or would the x=20, y=50; x=25, y=50; & x=30, y=50 be linear? Or is it because of the constant at the end that none of it is linear?"
You present only one Table, and it is not linear. Each entry is not a table
Okay...now I understand. Thank you very much!!
In order to determine whether the relationship in the given table is linear, we need to analyze the pattern and behavior of the values in the table.
Looking at the y-values, we can see that they start increasing as we move from x = 5 to x = 20, but then they remain constant at y = 50 for x values greater than or equal to 20. This indicates a sudden change in the behavior of y, which suggests a non-linear relationship.
To further confirm whether any part of the table represents a linear relationship, we can calculate the differences between consecutive y-values for different intervals of x. Let's calculate the differences for two intervals: x = 5 to x = 15, and x = 20 to x = 30.
For the first interval (x = 5 to x = 15):
Difference in y: 40 - 20 = 20
Difference in x: 15 - 5 = 10
For the second interval (x = 20 to x = 30):
Difference in y: 50 - 50 = 0
Difference in x: 30 - 20 = 10
The differences in y-values for both intervals are not constant, indicating a non-linear relationship. Therefore, none of the parts of the given table represent a linear relationship.
In conclusion, the entire table does not exhibit a linear relationship because the y-values change suddenly and do not follow a consistent pattern.