Step-by-step explanation:
take two point from the line;
taken lines are:-
(x1,y1)=(0,4)
(x2,y2)=(5,1)
equation for the line pictured below is:
(y-y1)=(y2-y1)(x-x1)/(x2-x1)
or, (y-4)=(1-4)(x-0)/(5-0)
or, (y-4)=-3×x/5
or, 5y-20=-3x
.•. 3x+5y=20----(1)
line perpendicular with line (1) is:
5x-3y+k=0----(2)
since line (2) passes through (-1,4);
5×(-1)-3×4+k=0
or, -5-12+k=0
or, -17+k=0
.•.k=17
and
the line that passes through (-1,4) and is perpendicular to the line pictured above is
5x-3y+12=0
