The slope of this line is
2-(-4) 6
m = ------------ = ------- = 3/2
2-(-2) 4
Starting with y = mx + b, we get 2 = (3/2)(2) + b, or b = -1
Then the equation is y = (3/2)x - 1. Now let's change this into standard form:
Mult all terms by 2: 2y = 3x - 2. Move 2y to the right side: 3x - 2y - 2 = 0. This is in standard form.