Confusing Bonus Question

Hi, everyone! My teacher created a bonus question on an assignment I'm completing.Do you have any idea what this means and how to solve it? Thanks!

1 Answer

Yes, Quadrant I provides the entire solution set for this question. Indeed for any given $c$, if we let $x=a$ and $y=b$, then $a+b=c^2$, translates to 
\[x+y=c^2  \Rightarrow  y=-x+c^2\]
which is a line with slope $m=-1$, and $x$-intercept and $y$-intercept are both $c^2$. 

For example for $c=5$ you get 
\[y=-x+25\]
which is the question of the red line in the image. 

Join Matchmaticians Affiliate Marketing Program to earn up to a 50% commission on every question that your affiliated users ask or answer.