What is (3,4) and (-6,-2) in slope intercept form

So first u find slope which in this case is 2/3 then u put it in the equation so y=2/3x+b

in order to find be which is the y intercept u have to plug in any of the points so 4=2/3*3+b

so 2/3*3 is 6/2 which is also 3 so 4=3+b

now what u want to do is subtract 3 from each side so its going to be 1=b so B=1

now we can write it. y=2/3x+1

please correct me if I'm wrong thank you