To find the [tex]x_i[/tex] intercept, set [tex]x_j=x_k=0[/tex]. By this I refer to the following procedure.
x-intercept: Set [tex]y=z=0[/tex], then you're left with [tex]4x=60\iff x=15[/tex]. Then the x-intercept is [tex](15,0,0)[/tex].
y-intercept: Set [tex]x=z=0[/tex], then [tex]-6y=60\iff y=-10[/tex]. The y-intercept is [tex](0,-10,0)[/tex].
z-intercept: Set [tex]x=y=0[/tex], then [tex]-5z=60\iff z=-12[/tex]. The z-intercept is [tex](0,0,-12)[/tex].
