If three points `A(h ,0),\ P(a , b)a n d\ B(0, k)` lie on a line, show that: `a/h+b/k=1.`

Explanation

Slope of line `AB=(0-b)/(h-a)=(-b)/(h-a)`
Slope of line `BC=(k-0)/(0-h)=(-k)/(h)`
Now, `A` , `B` and `C` are collinear.
`:.` slope of `AB=` slope of `BC`
`implies (-b)/(h-a)=(-k)/(h)`
`implies -hb=-kh+ak`
`implies (-b)/(k)=-1+(a)/(h)`
`implies (a)/(h)+(b)/(k)=1`