Question

The equation of a line through (3,\,-4)
and perpendicular to the line 3x+4y=5
is [RPET 1981, 84, 86; MP PET 1984]
A) 4x+3y=24 B) y-4=(x+3) C) 3y-4x=24 D) y+4=\frac{4}{3}(x-3)

Answer 1

Line is perpendicular to the line 3x+4y=5; rearrange this as y=mx+c form;
y=(-3/4)x+(5/4);
Slope m1=-3/4; (m1*m2=-1 for perpendicular line
But this line is perpendicular to the line which is passing through(3,-4) So for this slope is m2=4/3;
So equation of line which is passing though a point (x1,y1) and slope is 4/3;
y+4=4/3(x-3)