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Which set of ordered pairs represents a linear relation. Explain your answer. {(0, 3600), (4, 3526), (8, 3353.5), (12, 3147.5)) or ((15, 2988.5), (21, 2670.5), (27, 2352.5), (33, 2034.5)} ​

User Njuffa
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Answer:

{(15, 2988.5), (21, 2670.5), (27, 2352.5), (33, 2034.5)}

Explanation:

Let's analyze both sets of ordered pairs:

Set 1: {(0, 3600), (4, 3526), (8, 3353.5), (12, 3147.5)}

The x-values in this set increase by a constant amount of 4: 0, 4, 8, 12.

Now let's examine the corresponding y-values:

3600, 3526, 3353.5, 3147.5

To determine the rate of change between the y-values, we subtract consecutive pairs:

3526 - 3600 = -74

3353.5 - 3526 = -172.5

3147.5 - 3353.5 = -206

The y-values in this set decrease, but the rate of change is not constant. The differences between consecutive y-values are not the same, indicating that the relation is not linear.

Set 2: {(15, 2988.5), (21, 2670.5), (27, 2352.5), (33, 2034.5)}

The x-values in this set also increase by a constant amount of 6: 15, 21, 27, 33.

Now let's examine the corresponding y-values:

2988.5, 2670.5, 2352.5, 2034.5

Again, we calculate the differences between consecutive y-values:

2670.5 - 2988.5 = -318

2352.5 - 2670.5 = -318

2034.5 - 2352.5 = -318

In this set, the y-values decrease by a constant rate of 318. The rate of change between consecutive y-values is the same, indicating that the relation is linear.

Therefore, the set of ordered pairs {(15, 2988.5), (21, 2670.5), (27, 2352.5), (33, 2034.5)} represents a linear relation.

User Mvb
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