To write the equation of a line, we need 1) a point on the line 2) it's slope
For the point, we just substitute in the equation of the line intersecting it with x=3 (because they share this point)
Therefore, 2*3-3y=6 --> That gives y=0
Then the point is (x1,y1)=(3,0)
We already have the slope : m=2
Now we should use this relation for the required line equation
(y-y1) / (x-x1) = m
Then (y-0) / (x-3) = 2
Then y = 2*x - 6
And that is the required form
where 2 is the slope and -6 is the intercept
