Question

Find the intercepts and sketch the graph of the plane. $$ x+y-z=0 $$

Short answer

The x-intercept, y-intercept, and z-intercept of the plane equation \(x+y-z=0\) are all at the origin (0, 0, 0). The graph of this plane is a plane passing through the origin, cutting the x, y, and z axes at this point.

Step-by-step solution

Finding the X-intercept

For the x-intercept, set y and z equals to zero in the equation. You're left with \(x=0\). Thus, the x-intercept is at the point (0, 0, 0).

Finding the Y-intercept

For the y-intercept, set x and z equals to zero in the equation. You will be left with \(y = 0\). Thus, the y-intercept is at the point (0, 0, 0).

Finding the Z-intercept

For the z-intercept, set x and y equals to zero in the equation. You will be left with \(-z = 0\), which simplifies to \(z=0\). Thus, the z-intercept is at the point (0, 0, 0).

Sketching the graph

All intercepts are at the origin (0,0,0). The graph will be a plane passing through the origin. It will slice all three coordinate axes at the origin.