Given two points on a line, use the formula below to find its equation
[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} (5,2),(10,-3) \\ \Rightarrow y-2=\frac{-3-2}{10-5}(x-5) \\ \Rightarrow y-2=-\frac{5}{5}(x-5) \\ \Rightarrow y-2=-(x-5)=-x+5 \\ \Rightarrow y=-x+5+2 \\ \Rightarrow y=-x+7 \end{gathered}[/tex]Thus, the equation is y=-x+7
