Find a relation between x and y, if the points A(x, y), B(−5, 7) and C(−4, 5) are collinear.

Let A(x1 = x, y1 = y), B(x2 = −5, y2 = 7) and C(x3 = −4, y3 = 5) be the given points.
The given points are collinear if

$x_{1}\left(y_{2}-y_{3}\right)+x_{2}\left(y_{3}-y_{1}\right)+x_{3}\left(y_{1}-y_{2}\right)=0$

$\Rightarrow x(7-5)+(-5)(5-y)+(-4)(y-7)=0$

$\Rightarrow 7 x-5 x-25+5 y-4 y+28=0$

$\Rightarrow 2 x+y+3=0$

Hence, the required relation is 2x + y + 3 = 0.