The equation of the line passing through the points $(4,2)$  and perpendicular to the line joining points $(0,0)\text{\hspace{0.17em}and\hspace{0.17em}}(-1,5)$  is

Let $A(0,0),B(-1,5)$

Equation of $AB$  is $y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

$\begin{array}{l}y-0=\left(\frac{5-0}{-1-0}\right)(x-0)\\ y=-5x\\ 5x+y=0\end{array}$

Equation of line passing through point $(4,2)$  and perpendicular to $5x+y=0$ is $1(x-4)-5(y-2)=0$

$\begin{array}{l}x-4-5y+10=0\\ x-5y+6=0\end{array}$