Question

Use a system of equations to solve the problem.
There is an initiation fee to join the Pine River Country Club, as well as monthly dues. The total cost after 7 months' membership will be $3,050, and after 1-1/2 years, $3,930. Find both the initiation fee and the monthly dues.

Answer 1

think of this as 'find the equation for the line through the points \[(7,3050),(18,3930)\]
the 18 because one and a half years is 18 months. the slope is the monthly dues, the y-intercept (what you get when x = 0) is the initiation fee.

Answer 2

\[m=\frac{3930-3050}{18-7}=\frac{880}{11}=88\]
so it is $88 a month.

Answer 3

to find the y-intercept write \[y-y_1=m(x=x_1)\]
\[y-3050=88(x-7)\]
\[y-3050=88x-616\]
\[y=88x+2434\]
initiation fee is $2434