Question

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

Answer 1

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).

Answer 2

The intercepts are:

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

Explanation:

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)