Question

How do i do this?
Graph -x+2y+2z=6

Answer 1

Have you ever graphed 3D?

Answer 2

Draw 3 axes instead of 2 like you're used to, and label them x, y, and z. Then you need to use substitution to get your values for each variable.

Answer 3

So first I would solve for x in terms of y and z by isolating it. x=2y+2z-6

Answer 4

Then do the same and solve for y next in terms of z. Once you have that answer, solve for z now that you have all z's and then proceed to plug in your number value for z into the previous equations for x and y.

Answer 5

x = 0 for all points on the yz plane.
y = 0 for all points on the xz plane.
z = 0 for all points on the xy plane.

So set x = 0 in you equation and you will get the equation of a straight line in the yz plane. Draw that line.

Do the same on the other two planes.

The graph of -x+2y+2z=6 will be a plane containing all those three lines drawn earlier.

Answer 6

Actually I think my method is broken here, just ignore what I said.

Answer 7

-x+2y+2z=6
set x = 0. 2y+2z = 6, y + z = 3. Draw this line on the yz plane

set y = 0. -x + 2z = 6. Draw this line on the xz plane

set z = 0. -x + 2y = 6. Draw this line on the xz plane

Answer 8

Just thought of something: You can simplify the graphing even further by setting two of the coordinates at a time to zero.

-x+2y+2z=6

Set x = 0, y = 0: 2z = 6 ; z = 3 This is where the plane cuts the z axis.
Set x = 0, z = 0: 2y = 6 ; y = 3 This is where the plane cuts the y axis.
Set y = 0, z = 0: -x = 6 ; x = -6 This is where the plane cuts the y axis.

Knowing three points, is enough to determine the plane. So draw a plane passing through those three points.

The sketch does not depict the entire plane but just shows where the plane intersects the x,y,z axes and the xy, yz, xz planes.