Finding the equation of aline in implicit form

Question

If I am given two points, (-2,0) and (0,-1), how do I find the equation of the line in implicit form that passes through these two points? Additionally, how do I convert that equation to point-normal form? i.e N * (x-p) = 0?

Answer 1

Let the equation of the line is $y=ax+b$. When $x=0, y=-1$, $b=-1$. Now we have the equation $y=ax-1$. Now we substitute $x=-2, y=0$, $0=-2a-1$, and $2a=-1$, so $a=0.5$. We have the equation $y=0.5x-1$.