Let [tex]c[/tex] be the amount of parts the student answered correctly. Suppose that [tex]s(c)[/tex] is a function between [tex]c[/tex] and the score of a student's project. As the student initially receives a fixed [tex]50[/tex] points for turning the project in and [tex]5[/tex] points for each correct part, the function is initially:
[tex]s(c) = 5c+50[/tex]
When the students receive [tex]7[/tex] points for each correct part, the coefficient of [tex]c[/tex] changes, as the amount of points received per correct answer increases. Thus:
[tex]s(c) = 7c+50[/tex].
