if three points (h,0), (a,b) and (0,k)lie on a line, show that a/h + b/k =1

lets call them A,B,C respectively.

since they lie on the same line, so

slope of AB=slope of BC=slope of AC

slope of AB=b-0/a-h..(i)

slope of BC=k-b/0-a..(ii)

slope of AC=k-0/0-h..(iii)

from (i) and (iii0 we get

b/a-h=k/-h

so

b(-h)=k(a-h)

i e.

-bh=ak-kh

i.e.

ak+bh=kh

dividing by kh both sides,

a/h  +b/k  =1

 hence the answer.