# Math Help - Intersection point of a line and a plane

1. ## Intersection point of a line and a plane

Find the point where $\frac{x-2}{5} = y = \frac{z+1}{3}$ intersects $x+y-z=2.$

??

2. Originally Posted by Em Yeu Anh
Find the point where $\frac{x-2}{5} = y = \frac{z+1}{3}$ intersects $x+y-z=2.$
Write the line as $\left\{ \begin{gathered} x(t) = 5t + 2 \hfill \\
y(t) = t \hfill \\ z(t) = 3t - 1 \hfill \\ \end{gathered} \right.$

Now substitute into the plane and then solve for t.