# An office machine purchased new for \$3600 loses \$400 each year.

Assume the value continues to decrease the same amount each year. If f(x) represents the value of the office machine after x years, which linear function models the given situation?

A) f(x) = 400x + 3600 B) f(x) = −400x − 3600 C) f(x) = −400x + 3600 D) f(x) = 400x − 3600

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1879698

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## No, the correct answer is D) f(x) = 400x - 3600.

The slope (-400) represents the amount the value decreases each year, and since it is negative, the function needs to subtract that value each year. The y-intercept (3600) represents the initial value of the machine, so it should be added to the slope. Therefore, the equation of the linear function is:

f(x) = -400x + 3600

By simplifying this equation, we get:

f(x) = 400x - 3600

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## Well, let's think about this situation. We know that the office machine loses \$400 each year. If we start with \$3600, and subtract \$400 each year, we can model that with the equation f(x) = -400x + 3600.

So the correct answer is C) f(x) = -400x + 3600. It looks like our office machine is not appreciating in value! Better put a "Do Not Touch" sign on it to protect its feelings.

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## To solve this problem, we need to find a linear function that models the given situation.

We are told that the office machine loses \$400 each year. This means that the value of the machine decreases by \$400 after each year.

Let's break down the given information:
- After 1 year, the machine loses \$400, so the value is \$3600 - \$400 = \$3200.
- After 2 years, the machine loses another \$400, so the value is \$3200 - \$400 = \$2800.
- After 3 years, the machine loses another \$400, so the value is \$2800 - \$400 = \$2400.

Looking at these values, we can see a pattern: the value of the machine decreases by \$400 with each passing year. So, for every year x, the machine loses \$400x.

Now, let's look at the options:
A) f(x) = 400x + 3600
B) f(x) = -400x - 3600
C) f(x) = -400x + 3600
D) f(x) = 400x - 3600

Since the value of the machine is decreasing each year, the function should have a negative coefficient for x.

Out of the given options, the correct answer is C) f(x) = -400x + 3600, as it has the negative coefficient (-400x) and correctly models the situation where the machine loses \$400 each year.

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## you have the slope (-400) and the y-intercept (3600)

so, what do you think?