Step-by-step explanation:
We have got the lines :

Both lines intercept the x-axis in the point :

In all point from x-axis the y-component is equal to 0.

We replace the I point in the lines equations:

From the first equation :

From the second equation :

Then 
Finally :

y = ax + b and y = cx + d have the same x-intercept ⇔ad=bc
This is TRUE!
The definition for perpendicular only applies when the lines are at a right angle which is 90°