# Vectors and line equations and planes

Which of the three coordinate planes does the line given by $$x=16t, y=-4-9t, z=34$$ intersect?

I am confused where to start with this question. I was thinking maybe to solve $$t$$ from equation of $$y$$ but I am unsure.

• For example, to see if it intersects the $y$-$z$ plane, this is when the other variable is $0$, i.e. $x=0$. So you need to see if $x=0$ is possible on your line. Similarly for the other two coordinate planes. – Minus One-Twelfth Mar 21 at 22:52
• Oh okay, thank you – user221435 Mar 21 at 22:54
• HINT: If $z=34$, the line is contained in a plane parallel to the $xy$-plane. – Ted Shifrin Mar 22 at 0:09