Math Help - Where does the plane intersect the axis?

1. Where does the plane intersect the axis?

Find the points at which the plane 3x-4y+z=12 intersects the coordinate axis and find the equations of the lines where the plane intersects the coordinate planes.

2. Re: Where does the plane intersect the axis?

Find the points at which the plane 3x-4y+z=12 intersects the coordinate axis and find the equations of the lines where the plane intersects the coordinate planes.
To find the x-intercept set the y and z coordinates equal to zero. This gives

$3x-4(0)+0=12 \iff x=4 \iff (4,0,0)$

Now do the same thing with y and z, set the other two coordinates to zero.

To find the equation of the line in the xy plane, set $z=0$

This gives

$3x-y=12 \iff y=3x-12$

Again do the same thing with the other two coordinates.