IS. 2 Given four points $R(0,0), S(a, 0), T(a, 6)$ and $U(0,6)$. If the line $y=b(x-7)+4$ cuts the quadrilateral $R S T U$ into two halves of equal area, find the value of $b$.
$y=b(x-7)+4$ represents a family of straight lines with slope $b$ which always pass through a fixed point $A(7,4)$. $R(0,0), S(20,0), T(20,6)$ and $U(0,6)$. $R S T U$ is a rectangle whose base is parallel to $x$-axis with centre at $C(10,3)$.
The line joining $A C$ bisect the area of the rectangle. $b=\frac{3-4}{10-7}=-\frac{1}{3}$