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September 20th, 2013, 06:27 AM   #1
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Help With Linear Equation Word Problem

I am having a really hard time understanding how this is done since the chapter we are on has to do with the slope-intercept form y=mx+b. This is the problem as follows:

A copier was purchased by a company for $7,500. After 5 years it is estimated that the value of the copier will be $4,500 . If the value in dollars V and the time the copier has been in use t are related by a linear equation, find the equation that relates V and t.

I kind of understand how I could graph this into a line and then find a y-intercept point and then create an equation but at the same time I don't. Can anyone break it down for me or help me by pushing me in the right direction. I have a ton more of the these word problems and I'm sure if I can understand this one I can get all the rest done on my own. Thanks!
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September 20th, 2013, 06:38 AM   #2
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Re: Help With Linear Equation Word Problem

You are given that V and t have a linear relationship. The first step, therefore, is to let:

V(t) = mt + b (1)

This is the general form of a linear equation.

Next, you are given V for two values of t:

When t = 0, V(0) = $7500

When t = 5, V(5) = $4500

So, if we put t = 0 into the equation (1) above, we get:

V(0) = b

Therefore b = 7500

Next we put t = 5 and v(5) = 4500 into the equation at (1) to get:

4500 = 5m + 7500

Therefore 5m = -3000, so m = -600

So, the equation is:

V(t) = -600t + 7500
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September 20th, 2013, 12:55 PM   #3
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Re: Help With Linear Equation Word Problem

Ahhhhh. Makes much more sense now that you put it in those words. This online courses e-text is extremely vague and really only has examples but nothing of the word problems I've ran into in the HW assignments. I appreciate the help the rest should be easy peasy now.
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