Orthogonality & Least Squares · Medium problem

A scientist fits a proportional model $y=mx$ (through the origin) to data that is noisier at some points, so each squared error is weighted by a reliability weight $w$. For the triples $(x,y,w) = (1,2,3), (2,4,1), (3,1,2)$, the weighted least-squares slope is $m = \dfrac{\sum w_ix_iy_i}{\sum w_ix_i^2}$. Find $m$.