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

The intercepts are:

     (20,0,0)  , (0,8,0) and (0,0,-10)

We know that the intercept of a function are the points where it meets the axis.

i.e. x-intercept is the point where  both the y and z value is equal to zero.

y-intercept is the point  both the x and z value is equal to zero.

z-intercept is the point where  both the x and y value is equal to zero.

The equation is given by:

            2x+5y-4z=40

Now we calculate:

x-intercept:

we put y=z=0 in the equation, to get:

    2x=40

i.e. x=20  ( Since on dividing both side by 2)

Hence, x-intercept is: (20,0,0)

y-intercept:

we put x=z=0 in the equation, to get:

    5y=40

i.e. y=8  ( Since on dividing both side by 8)

Hence, y-intercept is: (0,8,0)

z-intercept:

we put y=x=0 in the equation, to get:

    -4z=40

i.e. z= -10  ( Since on dividing both side by -4)

Hence, z-intercept is: (0,0,-10)