$\text{ Suppose that }a,b(a>b)\text{ are the roots of the equation }{x}^2-5x+4=0\text{ then the }$

$\text{ equation of the line passing through the point }(a,b)\text{ and having the slope }\frac{a}{b}\text{ is }$

$\text{ Split the middle term to find the roots of the equation }{x}^2-5x+4=0$

It implies 

$\begin{array}{c}{x}^2-x-4x+4=0\\ x\left(x-1\right)-4\left(x-1\right)=0\\ \left(x-1\right)\left(x-4\right)=0\end{array}$

$\text{ The roots of the equation }{x}^2-5x+4=0\text{ are }a=4,b=1$

$\text{ Equation of line passing through the point }\left(x_1,y_1\right)\text{ and having slope }m\text{ is }y-y_1=m\left(x-x_1\right)$

$\text{ Hence the equation of line passing through the point }(4,1)\text{ and having the slope }m=4\text{ is as }$$\text{below}$

$\begin{array}{c}y-1=4\left(x-4\right)\\ y-1=4x-16\\ 4x-y-15=0\end{array}$

$\text{ Therefore, the equation of the required line is }4x-y-15=0$