The equation of the straight line passing through the foot of the perpendicular of (4, 5) on to x-axis and image of the same point w.r.t. y-axis is 

Let P is foot of perpendicular of A (4, 5) on X- axis , P= ( 4, 0)

And Q is Image of A (4, 5) w.r.to Y-axis , Q ( -4, 5)

Equation of PQ

 $\begin{array}{l}\Rightarrow y-0=\frac{5-0}{-4-4}\left(x-4\right)\\ \Rightarrow y=\frac{5}{-8}\left(x-4\right)\\ \Rightarrow -8y=5x-20\\ \Rightarrow 5x+8y-20=0\end{array}$