What are the intercepts of 2x+5y-4z=40

In order to find x-axis interception coordinates you need to set other two variables (y and z) to zero and solve the remaining equation.

So the following simple equations need to be solved:

2x = 40

5y = 40

-4z = 40

It intercepts x-axis at coordinates (20; 0; 0), y-axis at (0; 8; 0) and z-axis at (0; 0; -10).