The line to be found is parallel to 4x - 3y = 7. The slope of 4x - 3y = 7 can be found by rewriting this as
3y = 4x - 7
=> y = (4/3)x - 7
Therefore the slope of the line is (4/3).
Therefore the equation of the line is y = (4/3)x + k
=> 4x - 3y + 3k = 0
The required line passes through a point which is at a distance 4 from (1, -2).
We use the relation for determining the distance d of a point (x1, y1) from the line ax+by +c = 0, which is:
d = |ax1+by1+c|/ sqrt (a^2+b^2)
4 = |4 + 6 + 3k|/ sqrt (16+9)
20 = 10 + 3k
=> 3k = 10
Therefore the equation of the required line is 4x -3y + 10 = 0.