Let $A\left(x_{1}=2, y_{1}=1\right), B\left(x_{2}=x, y_{2}=y\right)$ and $C\left(x_{3}=7, y_{3}=5\right)$ be the given points The given points are collinear if

$\mathrm{x}_{1}\left(\mathrm{y}_{2}-\mathrm{y}_{3}\right)+\mathrm{x}_{2}\left(\mathrm{y}_{3}-\mathrm{y}_{1}\right)+\mathrm{x}_{3}\left(\mathrm{y}_{1}-\mathrm{y}_{2}\right)=0$

$\Rightarrow 2(y-5)+x(5-1)+7(1-y)=0$

$\Rightarrow 2 y-10+4 x+7-7 y=0$

$\Rightarrow 4 \mathrm{x}-5 \mathrm{y}-3=0$

Therefore, the required relation is $4 \mathrm{x}-5 \mathrm{y}-3=0$.