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The point a will always lie on the line,

y-a = m(x-a)

where m is the slope of the line

y-a = m(x-a)

where m is the slope of the line

The point is (a,a)

taking the equ. x+y=0

putting x=a, y=a

=> L.H.S x+y=a+a=2a=R.H.S

so point (a, a) lies on the equ. x+y=2a