You can easily write the equation of the line you have in this form: y= -3x +7.
Then the condition for a line to be perpendicular to a given line is that its gradient multiplied by the gradient of the given line must give - 1 as result.
The given line has gradient 3, then the gradient of the perpendicular line must be - 1/3, since 3 multiplied -1/3 is equal to -1.
To this condition you have to add the passage through the point (4;3) which is:
y - 3=-1/3 * (x-3) which leads to
y= -x/3 + 1
and that's the equation of the perpendicular line passing through (4;3)