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

<pre><font size = 4 color = "indigo"><b>
>>...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 

({{{x1}}},{{{y1}}}) = (2,8762), and ({{{x2}}},{{{y2}}}) = (5,12421)

First we find the slope from the formula
     
{{{m=(y2-y1)/(x2-x1)=(12421-8762)/(5-2) = 3659/3}}}

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:

{{{y-y1=m(x-x1)}}}

Substituting for {{{y1}}},{{{m}}}, and {{{x1}}}

{{{y-8762=(3659/3)(x-2)}}}

Clear of fractions by multiplying by 3

{{{3y-26286=3659(x-2)}}}

Distribute on the right

{{{3y-26286=3659x-7318}}}
 
Add 28286 to both sides

{{{3y = 3659x + 18968}}}

Divide thru by 3

{{{(3y)/3 = 3659/3}}}{{{x + 18968/3}}}

{{{y = 3659/3}}}{{{x + 18968/3}}}

Now we only need to change the {{{x}}} to an {{{m}}}
and the {{{y}}} to an {{{S}}}.

{{{S = 3659/3}}}{{{m + 18968/3}}}

Edwin</pre>