Question

Which table could be a partial set of values for a linear function?

x y
0 0
1 2
2 8
3 18

x y
0 3
1 5
2 7
3 9

x y
0 9
1 8
2 5
3 0

x y
0 1
1 2
2 5
3 10

Answer 1

The second table is correct.

x y

0 3

1 5

2 7

3 9

Explanation:

Answer 2

The second table

Explanation:

When x-values are uniformly spaced (1 apart, for example), y-values are also uniformly spaced (have a common difference) when the function is linear.

The second table shows a common difference of 2 between y-values, so that function is linear.

_____

Table 1 differences are 2, 6, 10, so is likely quadratic.

Table 3 differences are -1, -3, -5, so is likely quadratic.

Table 4 differences are 1, 3, 5, so that one, too, is likely quadratic.

_____

Comment on differences

We call the differences between table values the "first differences." Then the differences between those are "second differences." Differences between the "n-1-th" differences are called the "n-th" differences. When n-th differences are constant (and not zero), the table values can be represented by a polynomial of n-th degree.

Hence when 1st differences are constant, the table represents a 1st-degree (linear) function. When 2nd differences are constant, the table represents a quadratic function.