The table shows the relationship between the number of minutes someone was watching traffic and the total number of blue cars she saw.
Minutes Blue Cars
10 3
14 5
18 10
22 13
Is the relationship a function that is increasing or decreasing? Is the relationship a function that is linear or non-linear?
(1 point)
Responses
Increasing; linear
Increasing; non-linear
Decreasing; linear
Decreasing; non-linear
Increasing; non-linear
To determine whether the relationship between the number of minutes someone was watching traffic and the total number of blue cars she saw is increasing or decreasing, we need to look at how the values change.
If we observe the table, we can see that as the number of minutes increases, the total number of blue cars also increases. For example, at 10 minutes, the number of blue cars is 3. At 14 minutes, it increases to 5. At 18 minutes, it further increases to 10. And at 22 minutes, it becomes 13.
Therefore, we can conclude that the relationship is increasing.
Now, let's determine if the relationship is linear or non-linear. For a relationship to be linear, the ratio of change in the dependent variable (total number of blue cars) to the change in the independent variable (number of minutes) must remain constant.
If we calculate the ratio of change for each successive pair of data points, we get the following values:
(5-3)/(14-10) = 2/4 = 0.5
(10-5)/(18-14) = 5/4 = 1.25
(13-10)/(22-18) = 3/4 = 0.75
Since the ratios of change are not constant, the relationship is not linear.
Therefore, the correct answer is: Increasing; non-linear.