An operation is linear if it behaves "nicely" with respect to multiplication by a constant and addition. The name comes from the equation of a line through the origin, f(x)=mxf(x)=mxf(x)=mx, and the following two properties of this equation. First, f(cx)=m(cx)=c(mx)=cf(x)f(cx)=m(cx)=c(mx)=cf(x)f(cx)=m(cx)=c(mx)=cf(x), so the constant ccc can be "moved outside" or "moved through" the function fff. Second, f(x+y)=m(x+y)=mx+my=f(x)+f(y)f(x+y)=m(x+y)=mx+my=f(x)+f(y)f(x+y)=m(x+y)=mx+my= f(x)+f(y), so the addition symbol likewise can be moved through the function