Prove that the points `A(4,1)`, `B(-2,3)` and `C(-5,4)` are collinear. Also find the equation of the line passing through these points.

Explanation

Equation of a line passing through `A` and `B` points
`y-1=(3-1)/(-2-4)(x-4)`
`implies y-1=-(1)/(3)(x-4)`
`implies 3y-3=-x+4`
`implies x+3y=7`
and equation of a line passing through `B` and `C` points
`y-3=(4-3)/(-5-(-2))(x+2)`
`implies y-3=(1)/(-3)(x+2)`
`implies -3y+9=x+2`
`implies x+3y=7`
Therefore, the equations of `AB` and `BC` are same.
`implies A`, `B` and `C` are collinear.
Now, the equation of the line is
`x+3y=7`.