Question

Which of the following tables represents a linear function?

x= 1 1 0 1 1
y= −2 −1 0 1 2
,
x= 0 1 2 3 4
y= −3 2 0 −2 3
,
x= −2 −1 0 1 2
y= 2 0 −1 0 2
,
x= −2 −1 0 1 2
y= 3 1 −1 −3 −5

Answer 1

A linear function is one where the relationship between the variables can be represented by a straight line. Let's analyze the given tables to determine which one represents a linear function.

Table 1:
x = 1 1 0 1 1
y = −2 −1 0 1 2

Table 2:
x = 0 1 2 3 4
y = −3 2 0 −2 3

Table 3:
x = −2 −1 0 1 2
y = 2 0 −1 0 2

Table 4:
x = −2 −1 0 1 2
y = 3 1 −1 −3 −5

Looking at the tables, we can see that Table 2 represents a linear function. The relationship between x and y in Table 2 follows a consistent pattern where the values of y can be determined by a linear equation. The other tables do not show a consistent linear relationship between x and y.

Therefore, the correct answer is:

x = 0 1 2 3 4
y = −3 2 0 −2 3