What are the intercepts of the equation 4x-6y-5z=60

To find the intercept of a variable in a equation with more than one variable, you need to equal the others variables to zero.

-> 4x -6y -5z = 60

-> X-Intercept:
To find the X intercept, equal the Y and Z values to 0.
(Y = 0; Z = 0)

4x -6(0) -5(0) = 60
4x = 60
x = 60/4
x = 15

-> Y-Intercept:
To the Y intercept it's the same thing, equal the another variable values to 0.
(X = 0; Z = 0)

4(0) -6y -5(0) = 60
-6y = 60
-y = 60/6
-y = 10        x(-1)
y = -10

-> Z-Intercept:
(X = 0; Y = 0)

4(0) -6(0) -5z = 60
-5z =60
-z = 60/5
-z = 12         x(-1)
z = -12

The intercepts for this equation (15,-10,-12).
Or: x = 15, y = -10, z = -12.