Question

What are the intercepts of the equation 7x-2y-14z=56?

Answer 1

The intercepts are

(8,0,0),(0,-28,0),(0,0,-4)

Explanation:

we have

`7x-2y-14z=56`

step 1

Find the x-intercept

The x-intercept is the value of x when the value of y and z are equal to zero

so

For y=0, z=0

substitute

`7x-2(0)-14(0)=56`

solve for x

`7x=56`

`x=8`

The x-intercept is (8,0,0)

step 2

Find the y-intercept

The y-intercept is the value of y when the value of x and z are equal to zero

so

For x=0, z=0

substitute

`7(0)-2y-14(0)=56`

solve for y

`-2y=56`

`y=-28`

The y-intercept is (0,-28,0)

step 3

Find the z-intercept

The z-intercept is the value of z when the value of x and y are equal to zero

so

For x=0, y=0

substitute

`7(0)-2(0)-14z=56`

solve for z

`-14z=56`

`z=-4`

The y-intercept is (0,0,-4)

therefore

The intercepts are

(8,0,0),(0,-28,0),(0,0,-4)