Answer:
Table 1
Step-by-step explanation:
For a function to be linear, equal changes in x must correspond to equal changes in y.
In all tables, the x values increase by 1, so all changes in x in all 4 tables are 1.
If a function is linear, then all changes in y must be equal.
Table 1:
5 - 6 = -1
4 - 5 = -1
3 - 4 = -1
All changes in y are equal, so the first table is linear.
Table 2:
4 - 3 = 1
6 - 4 = 2
Two differences in y are different, so table 2 is not linear.
Table 3:
6 - 7 = -1
5 - 6 = -1
3 - 5 = -2
Not all differences in y are equal, so table 3 is not linear.
Table 4:
4 - 2 = 2
5 - 4 = 1
Not all differences in y are equal, so table 3 is not linear.
The only table that has equal differences in y corresponding to equal differences in x is Table 1, so only Table 1 shows a linear function.
