Consider the points $P(0,0), Q(4,0)$ and $R(1,2)$. The line with equation $y=m x+b$ is parallel to $P R$ and passes through the midpoint of $Q R$. What is the value of $b$ ?
The slope of $P R$ is $\frac{2-0}{1-0}=2$.

Therefore, the line that is parallel to $P R$ has the form $y=2 x+b$.

The midpoint of $Q R$ has coordinates $\left(\frac{4+1}{2}, \frac{0+2}{2}\right)$ which is the point $\left(\frac{5}{2}, 1\right)$.

Since the line with equation $y=2 x+b$ passes through the point with coordinates $\left(\frac{5}{2}, 1\right)$, then $1=2 \cdot \frac{5}{2}+b$, which gives $1=5+b$ and so $b=-4$.