The equation of the line x + 3y = 9 can be written in the slope intercept form y = mx + c as `y = -x/3 + 3` . The slope of this line is `-1/3` . As the product of the slope of perpendicular lines is equal to -1, the slope of a line perpendicular to x + 3y = 9 is 3.

If the perpendicular line passes through the point (3,0) its equation is `(y - 0)/(x - 3) = 3`

=> y = 3x - 9

The equation of the line perpendicular to x + 3y = 9 and passing through the point (3,0) is y = 3x - 9