The function $f$ is linear and satisfies $f(d+1)-f(d) = 3$ for all real numbers $d$. What is $f(3)-f(5)$?
I know that a linear function has the form $f(x) = ax + b$ for some constants $a$ and $b$. So I can substitute this form into the given equation and get $a(d+1) + b - (ad + b) = 3$. Simplifying this, I get $a = 3$, so $f(x) = 3x + b$. Now I want to find $f(3) - f(5)$, which is $3(3) + b - 3(5) - b$. The $b$'s cancel out, so I'm left with $9 - 15 = -6$. 