Question

How do we find the equation of line joining `A(0,0)` and `B(3,-3)`?

Answer 1

`x+y=0`

Explanation:

Method 1 - Equation of a line joining points `(x_1,y_1)` and `(x_2,y_2)` is given by

`(y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1)`

Hence equation of line joining `A(0,0)` and `B(3,-3)` is

`(y-0)/(-3-0)=(x-0)/(3-0)`

or `y/-3=x/3`

or `-y=x` i.e. `x+y=0`

Method 2 - As one point is `(0,0)`, `y`-intercept is `0` and hence equation is of type `y=mx`.

As it passes through`B(3,-3)`, we have

`-3=mxx3` or `m=-3/3=-1`

Hence equation is `y=-1xx x` or `y=-x` or `x+y=0`