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

Given points : `(h,0)`, `(a,b)`, `(0,k)`
Slope of a line passing through the points `(h,0)` and `(a,b)`
`m_(1)=(b-0)/(a-h)=(b)/(a-h)`
Slope of a line passing through the points `(A,b)` and `(0,k)`
`m_(2)=(k-b)/(0-a)=(b-k)/(a)`
If three points `(h,0)`, `(a,b)` and `(0,k)` are collinear, then `m_(1)=m_(2)`
`implies (b)/(a-h)=(b-k)/(a)`
`implies ab=ab=ak-bh+hk`
`impliesbh+ak=hk`
`implies (b)/(k)+(a)/(h)=1`