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### Linear Equations

Lines

Question One:   Below are the median market return and median stock

 Median Return for S&P 500 and Apple by   S&P 500 Return Tercile Tercile Median Market Return Median Apple Return 1 -0.0061 -0.0034 2 0.0124 0.0147 3 0.0285 0.0569
Median monthly returns from 1980 to 2017.   Data was sorted by smallest to largest S&P 500 returns and placed into terciles by S&P 500 return.

Consider the market return variable to be your X variable and the median Apple return to be your Y variable.   Provide an equation of the form Y=mx+b with the slope defined by the third and first quartile and with the line running through (X,Y) of the second tercile.

Answer to Lines Problem One:

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 to Lines Problem Two:

Question Three:   A gym offers two type of memberships.  The first membership has a \$200 up-front fee and a \$40 a monthly charge.   The second membership has a \$50 up-front fee and a \$70 monthly charge.   How many months must a person be a member of the gym in order for the first membership to be less expensive than the second membership?

Answer to Lines Problem Three