Word Problem

[Tiger-T]

Assume that the sales of a certain appliance dealer are approximated by a linear function. Suppose that sales were $ 3000 in 1982 and $ 87,500 in 1987. Let x = 0 represent 1982. Find the equation giving yearly sales S(x).

A) S(x) = 16,900x + 3000
B) S(x) = 84,500x + 3000
C) S(x) = 16,900x + 87,500
D) S(x) = 84,500x + 87,500

87,500 subtract 3,000 = 84,500
my guess is B

If not correct; how did you come up with your answer?

 

[galactus]

It is not B. You forgot to divide 84500 by 5. Do that and you're in good shape,

Since 1982 is the year 0, the year 1987 is x=5.

Then, the line passes through (0,3000), (5,87500)

Slope is \(\displaystyle \frac{y-y_{1}}{x-x_{1}}\)

 

[Denis]

You can always do a bit of "logical reasoning" first, like:
ok, this goes from 3000 to 87500 over 5 years;
that's an increase of 87500 - 3000 = 84500 over 5 years;
so that's an increase of 84500/5 = 16900 per year : get it?

 

[Tiger-T]

galactus and Denis,
I appreciate both of you so very much. So by the math I now beleive that the answer is C. Becuase it is figuring for yearly sales. S(x) = 16,900x + 87,500 should be the equation to represent the yearly sales, Correct??!!??

It is not B. You forgot to divide 84500 by 5. Do that and you're in good shape,

Since 1982 is the year 0, the year 1987 is x=5.

Then, the line passes through (0,3000), (5,87500)

Slope is \(\displaystyle \frac{y-y_{1}}{x-x_{1}}\)

 

[galactus]

No, not quite. Look at your y intercept. What is the value of y at x=0?.

 

[Tiger-T]

So it is A; correct. Becuase 16,500 (5) + 3000 = 85,500. 3000 should be the y-intercept. Sorry this is all new to me, and I am struggling.

 

[galactus]

Yep, you got it.

The slope is \(\displaystyle \frac{87500-3000}{5-0}=16900\)

This means sales went up 16900 per year.

At x=0, the sames are 3000. This is the y-intercept. Where the line crosses the y axis. The 'b' in y=mx+b.

The sales (in dollars) at the beginning, so to speak.

\(\displaystyle y=16900x+3000\)

That's it.

 

[Johnnyq]

That is a great example of real life application of slope. I always wondered about how can slope be used in real life. I was searching through bunch of sites and found explanation and calculators but no real life example. Below, is a link that actually has pretty good slope calculators if anyone ever wanna use it..
[spamming url edited out - SK]

 

[mmm4444bot]

Johnnyq: why are you posting on these boards?

Are you setting yourself up to begin SPAMMING?