Lines Problem Two

Question Two: A gym has a membership with both a lump sum annual fee denoted L and a per-time visit fee of  f.  The total amount spent by a member during a year is  denoted Y and the number of visits per year is denoted X.   The equation for total amount spent is of the form

Y=L+f*X

I have data on total amount spent and total number of visits for two people.

Visits	Dollars Spent
45	700
30	550

What is the value of L, the lump sum annual fee, and the value of f, the per-visit fee?

Answer: The slope of the line is 10 (700-550)/(45-30).   The line runs through (30,550) so solving for L we get 550-10*30 or L=250.

The equation for the line is

Y=250+10*X.

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