John wants to find the table that represents a linear function.
Which table represents a linear function?
Table 1
Table 2
Table 3
All of the choices
All of the choices could represent a linear function. It would depend on the values in each table. A linear function is one in which the rate of change is constant, meaning the difference between any two consecutive input values will be the same as the difference between their corresponding output values.
A linear function is a function whose graph is a straight line. In order to determine which table represents a linear function, we need to examine the values in each table.
If the values in a table exhibit a constant rate of change, then the function is linear. A constant rate of change means that the difference between the y-values (output values) for any two corresponding x-values (input values) is always the same.
Now, let's analyze each table to see if they exhibit a constant rate of change:
Table 1:
x | y
---------
1 | 3
2 | 5
3 | 7
Table 2:
x | y
---------
1 | 2
2 | 4
3 | 6
Table 3:
x | y
---------
1 | 2
3 | 5
5 | 8
In Table 1, the difference between the y-values for any two corresponding x-values is always 2. This indicates a constant rate of change, which is characteristic of linear functions.
In Table 2, the difference between the y-values for any two corresponding x-values is also always 2. This suggests a constant rate of change, indicating a linear function.
In Table 3, the difference between the y-values for any two corresponding x-values is not constant. For example, the difference between the y-values for x = 1 and x = 3 is 3 - 2 = 1, whereas the difference between the y-values for x = 3 and x = 5 is 8 - 5 = 3. This variability in the differences between y-values indicates a non-linear function.
Therefore, the tables that represent a linear function are:
- Table 1
- Table 2
In conclusion, both Table 1 and Table 2 represent linear functions.