1. The problem statement, all variables and given/known data Does the function: 4x-y=7 constitute a vector space? 2. Relevant equations All axioms relating to vector spaces. 3. The attempt at a solution x_n for example means x with the subscript n The book says that the function isn't closed under addition. So it continues by showing that given 2 points, (x_1,y_1) and (x_2,y_2) that when you add 4x_1-y_1=7 and 4x_2-y_2=7 you get 4(x_1+x_2)-(y_1+y_2)=14, how did they get the values for the problem to see that it sums to 14 and not 7? The case for multiplication show: 4x_1-y_1=7, they used 3 as the scalar to show: 3(4x_1-y_1)=12x_1-3y_1, that part makes sense, but then again they say that the right side is 3x7, and I don't see how they got those values.