Find a relation between x and y if the points ( x,y) , ( 1,2) and( 7, 0) are collinear (NOT BY AREA OF TRIANGLE METHOD)

Dear Student,
Solution) Given: (x,y) , (1,2) and (7,0) are collinear points. 
It means that the slope of any two points must be same.
Then,
​​​​$$\begin{gathered} \Rightarrow \frac{y-2}{x-1}=\frac{0-2}{7-1} \\ \Rightarrow \frac{y-2}{x-1}=\frac{-2}{6} \\ \Rightarrow 6(y-2)=-2(x-1) \\ \Rightarrow 6y-12=-2x+2 \\ \Rightarrow 6y+2x=2+12 \\ \Rightarrow 6y+2x=14 \\ \Rightarrow 2x+6y=14 \\ \Rightarrow x+3y=7 \end{gathered}$$
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Therefore,
for given points to be collinear, x and y must be related as:
x + 3y = 7
Regards!