Given
The line equation is

passes through the line (4,3 )
Find out the equation of the perpendicular line.
To proof
given equation is

the equation of line is in the form y = mx +c
where m = slope
c is the intercept on the y axis.
compare this equation to the above equation
we get

In perpendicular line case
The slope of a perpendicular line is the "negative reciprocal" of the slope of the original line.
thus slope of the perpendicular line
= 
Than equation perpendicular line becomes

as the line passes through the point( 4,3)
put these value in the above equation
we get

solving the above equation
3 +9 =c
12 =c
put this value in the above equation
we get

this is equation of the perpendicular line.
Hence proved