Question

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Answer 1

Answer:

3)

Step-by-step explanation:

An equation is linear if equal changes in x produce equal changes in y.

Let's look at each choice.

1)

A decrease of 10% per year. That means each year, the value of the car is 0.9 times the value of the previous year.

For example, if the original value was $10,000, after 1 year, it is worth 0.9 * $10,000 = $9,000. In 1 year it lost $1,000. In the next year, its value is now 0.9 * $9,000. The value at the end of the 2nd year is $8,100. In the second year, it lost $900 in value. In one period of 1 year it lost $1000 in value. In another equal period of 1 year, it lost $900 in value. A change of 1 year in time produces different changes in loss of value, so it is not linear.

2)

Here, the number doubles every year. Let's say it starts with 100 fish. After 5 years, it has 200 fish. In a change of 5 years in x, the change in y is 100. In the next 5 years, it goes from 200 fish to 400 fish. The change in the second period of 5 years is 200. We see that a change of 5 years can produce a change of 100 fish, but another change of 5 years can produce a change is 100 fish. Since for equal changes in x, the changes in y are not all equal, this is not linear.

3)

Here for every change of 1 day in x, the change in y is 2 liters. Each change of 1 in x always produces a change of 2 in y. This is linear.

4)

Each 2 hours, the amount of caffeine is 2/3 of what it was before. This is similar to the choice 1), and it is not linear.

Answer: 3)