Question

If f(0) = -2 and f(x + 2) - f(x) = 5, and f(x) is linear, what is the equation for f(x)?

Answer 1

We know:
\[
y=ax+b\\
-2=a(0)+b\\
b=-2
\]
So:\[
y=a(x+2)-2-(ax-2)=ax+2a-2-ax+2=2a=5\\
a=\frac{5}{2}
\]
So, we are done.