In general, given two points on a line, we can find its equation by using the formula below
[tex]\begin{gathered} (x_1,y_1),(x_2,y_2) \\ \Rightarrow y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \end{gathered}[/tex]Therefore, in our case,
[tex]\begin{gathered} (10,3),(13,-6) \\ \Rightarrow y-3=\frac{-6-3}{13-10}(x-10) \\ \Rightarrow y-3=-\frac{9}{3}(x-10) \\ \Rightarrow y-3=-3(x-10) \\ \Rightarrow y-3=-3x+30 \\ \Rightarrow3x+y=33 \end{gathered}[/tex]Thus, the answer is 3x+y=33, option C.
