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

Area of triangle = 1/2[x1(y2-y1) + x2(y3-y1) + x3(y1-y3)] = 1/2[x(7-5) + 5(5-y) - 4(y-7)]
Given A, B, and C are collinear, then the area of the triangle must be zero.
∴ 1/2[x(7-5) + 5(5-y) - 4(y-7)] = 0
⇒ 1/2[2x + 25 - 5y - 4y + 28] = 0
⇒ 1/2(2x - 9y + 53) = 0
Then, the relation between x and y is 2x - 9y + 53 = 0