Answer :

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

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