So if we have some constant k, then

\(\displaystyle{x}+{3}{y}+{5}{z}={k}\)

Recall that the equation of a plane is \(\displaystyle{a}{x}+{b}{y}+{c}{z}={d}\), with a surface normal of \(\displaystyle{<}{a},{b},{c}{>}\). Varying l wi;; result in different parallel planes. So f describes a familly of parallel planes.

Result: family of parallel planes