Given: The given line is 3x + 5y = 4. The perpendicular line has an x - intercept of - 3.

Formula to be used: The product of slopes of two perpendicular lines = - 1.

The slope of this line is .

the slope of the perpendicular line =

The equation of the line can be written in the form

(c is the y - intercept)

This line intercepts the x - axis when y = 0.

So, the x - intercept:

Now, it is given that the x - intercept is - 3.

i.e. c = 5

The required equation of the line is

i.e. 5x - 3y + 15 = 0