Question

Which of the following correctly indicates whether the set of ordered pairs {(1, 3), (2, 2), (3, 1), (4, 0)} satisfies the requirements for being a linear function and correctly explains why?

Answer 1

The set of ordered pairs {(1, 3), (2, 2), (3, 1), (4, 0)} satisfies the requirements for being a linear function.

Explanation:

Given the set of ordered pairs

{(1, 3), (2, 2), (3, 1), (4, 0)}

From the ordered pairs, we determine that:

x y

1 3

2 2

3 1

4 0

Determine the common difference of y-values:

• 2 - 3 = -1

• 1 - 2 = -1

• 0 - 1 = -1

As the common difference of y-values is same, it means the ordered pairs in the table represents the linear function.

In a nutshell,

• As there is no repetition of x values, it validates it indeed a function.
• The common difference of y-values is same, meaning it represents the linear function.

Please also check the attached graph. The graph is a straight line, further indicating that it is a linear function.

Therefore, the set of ordered pairs {(1, 3), (2, 2), (3, 1), (4, 0)} satisfies the requirements for being a linear function.