The tables that represents a linear function is "A 2-column table with 4 rows. Column 1 is labeled x with entries 3, 4, 5, 6. Column 2 is labeled y with entries 6, 5, 4, 3." Option 2
How do we find the table that represents a linear function?
1. For x values 3, 4, 5, 6 and y values 3, 4, 6, 7:
The changes in y are 4-3 = 1, 6-4 = 2, and 7-6 = 1.
Since the differences are not constant, this is not a linear function.
2. For x values 3, 4, 5, 6 and y values 6, 5, 4, 3:
The changes in y are 5-6 = -1, 4-5 = -1, and 3-4 = -1.
The differences are constant (-1), so this represents a linear function with a negative slope.
3. For x values 3, 4, 5, 6 and y values 7, 6, 5, 3:
The changes in y are 6-7 = -1, 5-6 = -1, and 3-5 = -2.
Since the differences are not constant, this is not a linear function.
4. For x values 3, 4, 5, 6 and y values 2, 4, 5, 6:
The changes in y are 4-2 = 2, 5-4 = 1, and 6-5 = 1.
Since the differences are not constant, this is not a linear function.