If three points (h,0), (a,b) and (o,k) lie on a line then

If given points lie on a line, thenh    0    1a    b    10    k    1=0Expanding along first row                 h(b−k)+1⋅(ak−b×0)=0⇒    bh+ak=hk⇒     ah+bk=1Alternatively:  Equation of the line joining (h,0) and (0,k) is xh+yk=1 as it makes intercepts h on x-axis and k on y-axisIf the point (a, b) also lies on it. thenah+bk=1