The equation of the perpendicular line is y = 3x/4 + 10/3
How to determine the equation of the perpendicular line
From the question, we have the following parameters that can be used in our computation:
4x + 3y = 10
In slope intercept form, we have
y = -4x/3 + 10/3
The slope of the above line is -4/3.
Perpendicular lines have slopes that are negative reciprocals of each other.
So, the perpendicular slope is 3/4.
The given line has a y-intercept of 10/3.
Since the perpendicular line has the same y-intercept as the given line, its y-intercept is also 10/3.
So, the line equation is
y = 3/4x + 10/3
Hence, the equation of the perpendicular line is y = 3x/4 + 10/3.