Question

find equation of lines which contains the point A(1,3)and the sum of whose intercepts on the co-ordinate axes is zero​

Answer 1

Given :

The equation passes through A(1,3)

Sum of x-intercept & y-intercept = 0

Point slope form of an equation;

y-y1 =m(x-x1)

y-3 =m(x-1)

Solve for y

y = mx - m -3

Y intercept x =0
y = -m-3

X intercept y = 0
x = m+ 3/ m

Therefore;
m+3/m -m-3 = 0
m+3 -m^2 -3m / m = 0
-m^2 -2m +3 = 0
m^2 + 2m - 3 = 0
(m+3) (m-1) =0
m = -3 and m=1

Two equations are;
y= mx -m -3
y = -3x +3 -3
y = -3x

And

y = x-1-3
y = x-4