Question

Find the relation between $x$ and $y$ if the points $(x,y),(1,2)$ and $(7,0)$ are collinear.

Answer 1

Since $A(x,y),B(1,2),C(7,0)$ are collinear

So, Slope of $AB=$ Slope of $BC$

$\Rightarrow \frac{2-y}{1-x}=\frac{0-2}{7-1}[\because m=\frac{y_2-y_1}{x_2-x_1}]\Rightarrow \frac{2-y}{1-x}=\frac{-1}{3}\Rightarrow 3(2-y)=-1(1-x)\Rightarrow 6-3y=x-1\Rightarrow x+3y-7=0$

Hence, the relation between $x$ and $y$ is $x+3y-7=0$