Question

Which of the following ordered pairs could be placed in the table and still have the relation qualify as a linear function?

Input Output
(x) (y)
1 12
3 9
5 6
? ?
A. (7, 3)
B. (7, 10)
C. (3, 3)
D. (3, 10)

Answer 1

Inputs form a sequence here: 1, 3, 5, 7

Outputs also form a sequence: 12, 9, 6, 3, with each being the previous numeral, less 3. So the 4th point would be (7,3).

Answer 2

A. (7, 3)

Explanation:

We are given a table.

Input (x) Output(y)

1 12

3 9

5 6

___ ___

The above table values form a linear equation.

In a linear relationship, difference between the x values are the same as well as the difference between the y values are the same.

Difference in x values = 3 - 1 = 3 and 6 - 3 = 2

So the difference between the x values is 2.

Difference in y values = 9 - 12 = -3 and 6 - 9 = -3

So the difference between the y values is -3.

So the next set of table values (7, 3)

Therefore, the answer is A. (7, 3)