Question

What's the intercepts for the equation 4x-6y-5z=60?

Answer 1

To find the $x_i$ intercept, set $x_j=x_k=0$. By this I refer to the following procedure.

x-intercept: Set $y=z=0$, then you're left with $4x=60\iff x=15$. Then the x-intercept is $(15,0,0)$.

y-intercept: Set $x=z=0$, then $-6y=60\iff y=-10$. The y-intercept is $(0,-10,0)$.

z-intercept: Set $x=y=0$, then $-5z=60\iff z=-12$. The z-intercept is $(0,0,-12)$.