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Question 141415: I am stuck on this linear equation story problem. I was hoping someone could please help me with the formula that I need.
A magazine subscription service sold 8762 subscriptions in February and 12, 421 subscriptions in May.
Assuming the number of subscriptions increased at a constant rate, write a linear equation to give the number of subscriptions S in terms of the month m. (Hint: Let the month of January be 1. Set the rest of the month values based on that starting point.)
I have x= Feb sales y= May sales n = number of months then y-x divided by n should give the rate of change. Am I on the right track?
This isn't from a book, it is from a problem in one of my online classes. Thanks so much ~Lyn
Answer by Edwin McCravy(20060)   (Show Source):
You can put this solution on YOUR website! I am stuck on this linear equation story problem. I was hoping someone could please help me with the formula that I need.
A magazine subscription service sold 8762 subscriptions in February and 12,421 subscriptions in May.
Assuming the number of subscriptions increased at a constant rate, write a linear equation to give the number of subscriptions S in terms of the month m. (Hint: Let the month of January be 1. Set the rest of the month values based on that starting point.)
I have x= Feb sales y= May sales n = number of months then y-x divided by n should give the rate of change. Am I on the right track?
This isn't from a book, it is from a problem in one of my online classes. Thanks so much ~Lyn
>>...8762 subscriptions in February...<<
This means
When the month was February, the number of subscriptions was 8762.
which means
When m = 2, S = 8762
which means that one point on the line of the graph is
(m, S) = (2, 8762)
-----
>>...12,421 subscriptions in May...<<
This means
When the month was May, the number of subscriptions was 12,421.
which means
When m = 5, S = 12,421
which means that another point on the line of the graph is
(m, S) = (5, 12421)
-------------------------------------
The problem now becomes:
Find the equation of the line which passes through the
points (2,8762) and (5,12421)
Let's temporarily replace m by x and S by y.
call the two points
( , ) = (2,8762), and ( , ) = (5,12421)
First we find the slope from the formula
Note that this is a different "m" from the "m" used in
the original problem. That m stood for month number,
but this m stands for the slope. But that won't cause
any difficulty since we will soon have a number for
the slope, and won't need m anymore for slope.
Now we use the point slope formula:
Substituting for , , and
Clear of fractions by multiplying by 3
Distribute on the right
Add 28286 to both sides
Divide thru by 3
 
Now we only need to change the  to an
and the  to an  .
 
Edwin
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