Well, basically what they are trying to do is isolate the y variable on the left side of the equation in order to get it in slope-intercept form (y=mx+b where "m" equals the slope and "b" is the y-intercept). So, in order to do this they have to do the inverse operations (so if it's adding they subtract, and if it's multiplying they divide.) Anyways, they do this with the intention of getting only the variable "y" on the left side of the equal sign. Once they did all that they got it in slope intercept form, and they know that the coefficient in front of the variable x is the slope.
