Sketching this Plane f(x,y) = y + 2x

[Saladsamurai]

Homework Statement

I am the worst human being ever right now. I cannot believe how much trouble I am having trying to sketch this by hand. I am used to just setting the coordinates equal to zero for 2 of them and finding the coordinate intercepts of the third; but that fails in particular case.

I tried to set up a table like so:

$$\begin{center} \begin{tabular}<br /> {| 1 | c | } <br /> \hline z & y = z - 2x \\ <br /> \hline 0 & y = -2x \\ <br /> \hline 1 & y = 1 - 2x \\<br /> \hline 2 & y = 2 - 2x \\ <br /> \hline \end{tabular} \end{center}$$

So I thought that "at" each value of z I could plot the line y = z - 2x and get something that works...but I cannot seem to make it happen.

For example: at z = 0, I would plot y = -2x, which is a line whose slope is -2 and whose y-intercept is 0.

at z = 2, I would plot y = 2 - 2x, which is the line whose slope is -2 and whose y-intercept is at 2.

It is just freaking me out that I have 2 lines with the same slope, yet they intercept y at different points.

Maybe someone can unconfuse me; but then again, maybe not.

 

[lanedance]

plot the line y = 2x in the xy plane (z=0), then z can take any value so the plane will bethe vertical extension of that line along the z axis.