Yes, this is a homework problem. I've included everything that I did. I got to the end, and I'm just off by a little bit. Probably just made a random little mistake somewhere that I can't catch.

Find the point of intersection of the line through and and the plane given by .

Here's what I've got...

Parametric equations of the line:

I substituted the parametric equations of the line into the equation of the plane...

Combining like terms I got and solved it to obtain

From here I substituted in the result...

Plugging these back into the equation for the plane, I obtained 1, not 2, and this is where my problem lies. I'm probably missing something obvious, so help would be much appreciated...