Mei's school is selling tickets to the annual talent show. On the first day of ticket sales the school
sold 7 senior citizen tickets and 1 child ticket for a total of $111. The school took in
$261 on the
second day by selling 14 senior citizen tickets and 5 child tickets. What is the price
each of one
senior citizen ticket?

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The graph of a proportional relationship is that of a straight line that passes through the origin (0,0).  It has the format y = kx, where k is the "constant of proportionality."     Linear functions of the form y = mx + b are NOT proportional relationships if b is not zero.