Question

Mrs. Mitchell decided to grade her projects by giving each student 50 points if they turned in a project and then an additional 5 points for each part they got correct. After looking through some of the projects, she decided to give the students 7 points for each correct section. If Mrs. Mitchell wrote a function to describe the situation, what would change?

Answer 1

Let $c$ be the amount of parts the student answered correctly.  Suppose that $s(c)$ is a function between $c$ and the score of a student's project.  As the student initially receives a fixed $50$ points for turning the project in and $5$ points for each correct part, the function is initially:

$s(c) = 5c+50$

When the students receive $7$ points for each correct part, the coefficient of $c$ changes, as the amount of points received per correct answer increases.  Thus:

$s(c) = 7c+50$.