I agree that this was a bit confusing. Higher up in the article, it shows that a linear function is one that doesn't change when scaled: F(a * x) = a * F(x)

I agree that this was a bit confusing. Higher up in the article, it shows that a linear function is one that doesn't change when scaled: F(a * x) = a * F(x) This is showing the relationship between two uses of the same function. Then, further along, we find: "So, what types of functions are actually linear? Plain-old scaling by a constant, or functions that look like: F(x)=ax In our roof example, a=1/3" I think in this second situation, F(x)=ax is not a relationship but rather a DEFINITION of the function F(x). In programming terms: function F(x: real) : real; begin Result := x * (1/3); end;