VTMO 2026 - Grade 8 - Semifinal - SET 06 - Self-study Question 2

The line $y=-ax+b$, with $a,b>0$, passes through $M=(1,2)$ and meets the coordinate axes at $A$ on $Ox$ and $B$ on $Oy$. When the area of triangle $OAB$ is as small as possible, find $a+b$.