Question

Which of these tables represents a linear function?

Answer 1

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.