Question
Determine if the table represents a linear function. If so, find the rate of change.
Answers
GPT 3.5
To determine if the table represents a linear function, we need to check if there is a constant rate of change between the values in the table.
If the rate of change between any two pairs of points in the table is the same, then the table represents a linear function.
For example, if the table contains the following points:
(1, 3), (2, 5), (3, 7), (4, 9)
By observing the differences in the y-values:
5 - 3 = 2
7 - 5 = 2
9 - 7 = 2
We can see that there is a constant rate of change of 2 between all pairs of points. Therefore, the table represents a linear function, and the rate of change is 2.
If the rate of change between any two pairs of points in the table is the same, then the table represents a linear function.
For example, if the table contains the following points:
(1, 3), (2, 5), (3, 7), (4, 9)
By observing the differences in the y-values:
5 - 3 = 2
7 - 5 = 2
9 - 7 = 2
We can see that there is a constant rate of change of 2 between all pairs of points. Therefore, the table represents a linear function, and the rate of change is 2.