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Dafna1 [17]
2 years ago
8

Which of the following correctly indicates whether the set of ordered pairs {(1, 3), (2, 2), (3, 1), (4, 0)} satisfies the requi

rements for being a linear function and correctly explains why?

Mathematics
1 answer:
Alekssandra [29.7K]2 years ago
4 0

Answer:

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

Step-by-step 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.

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==============================================================

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Check out the attached image. Using a red pen, I extended one of the lines to form a triangle. From the alternate interior angle theorem, we know that one of the angles of the triangle is 75 degrees (alternate interior angles are congruent). Again this stems from the fact that the lines are parallel.

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