How to show that a given line has a certain equation?

Question

Say line $A(3,0)$ and $B(0,2)$

How do I 'show' that they have equation $2x + 3y - 6 = 0$?

Answer 1

In two dimensional geometry, the equation of a line $(AB)$ where $x_A\not=x_B$ is $$y-y_B=\frac{y_B-y_A}{x_B-x_A}\left(x-x_A\right)$$ Just replace $x_A$, $x_B$, $y_A$ and $y_B$ by their values.

Answer 2

HINT: USE this

$$\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1}$$