Question

Equation of the line through the intersection of lines 2x+3y=4 and x-5y+7=0 which passes through the point ( -4,0) is

Answer 1

• Given line is:

2x+3y-4=0 ____(1)

x-5y+7=0 ______(2)

multiply by 2 in equ.(2) and subtract with equ (1),

we get,

2x-10y+14-2x-3y-4=0

y=-10/13

so, x=5y-7=-141/13

the intersecting point of these lines is (-141/13,-10/13)

so, the points are (-141/13,-10/13) and (-4,0)

slope of a line with two points is y1-y2/x1-x2

the slope is= -10/13-0/-141/13+4= 10/89

so,the equation of line is,

(y-0)=10/89(x+4)

10x-89y+40=0

therefore, required equation of line which passes through point(-4,0) is 10x-89y+40=0