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

(N/A) If the given points are collinear,then the area of the triangle formed by these points must be $0$.
The area of a triangle with vertices $(x_1, y_1), (x_2, y_2)$ and $(x_3, y_3)$ is given by the formula:
Area $= \frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|$
Substituting the given points $(x, y), (1, 2)$ and $(7, 0)$ into the formula:
$0 = \frac{1}{2} |x(2 - 0) + 1(0 - y) + 7(y - 2)|$
$0 = \frac{1}{2} |2x - y + 7y - 14|$
$0 = \frac{1}{2} |2x + 6y - 14|$
Multiplying by $2$ on both sides:
$2x + 6y - 14 = 0$
Dividing the entire equation by $2$:
$x + 3y - 7 = 0$
Thus,the required relation between $x$ and $y$ is $x + 3y - 7 = 0$.