Find the value of `x` for which the points `(x-1),\ (2,1)a n d\ (4,5)\ ` are collinear.

Explanation

Let `A=(x,-1)`, `B=(2,1)` and `C=(4,5)`
`:.` Slope of line `AB`,
`m_(1)=(1-(-1))/(2-x)=(2)/(2-x)`
and slope of line `BC`,
`m_(2)=(5-1)/(4-2)=(4)/(2)=2`
If three points are collinear then `m_(1)=m_(2)`
`implies (2)/(2-x)=2implies4-2x=2`
`implies-2x=-2impliesx=1`