In Heath-Brown's 2002 paper, "Rational points on curves and surfaces", he states

"We may observe that if $d \geq 3$, the surface $$x_1^d + x_2^d - x_2^{d-2} x_3 x_4 = 0$$ is absolutely irreducible, and contains no lines other than those in the planes $x_2 = 0, x_3 = 0$, and $x_4 = 0$."

I am wondering how he is able to be so conclusive as to state no other lines lie on the surface. Can anyone explain why this is 'obvious'?