Write the equation in slope-intercept form (-10,0) and (5,3) explain, i don't understand at all

Find the slope.  m = 
Find the y-intercept.  y = mx + b ⇒ y - mx = b
                                                        3 - =b
                                                        2=b
So the equation is y = 

So the first thing we do is to multiply the top equation by 3. the reason i want to do this is i notice there will be a 6y on both equations and can possibly add/subtract them. so we get 6y = -3x + 27. adding that and the second equation we get 6x = 27-15 which is 12. divide by 6 and we get 2. ∴ x = 2. substituting 2 into the first equation we get 2y = -2 + 9 which is 7. divide by 2 and we get 7/2. ∴ y = 7/2, x = 2.