Question

What are the intercepts of 2x + 3y – 6z = 30?

Answer 1

Intercept of equation 2x + 3y - 6z = 30 is (15, 0, 0) , (0, 10, 0) and (0, 0, -5)

Solution:

Given equation is:

2x + 3y - 6z = 30

We have to find the intercepts

Intercept are the point where equations cut the x- axis, y- axis and z- axis.

Thus, at x- axis :

y and z both are zero

So substitute y = 0 and z = 0 in given equation

2x + 3(0) - 6(0) = 30

2x = 30

x = 15

Thus the intercept is (15, 0, 0)

Thus at y - axis:

x and z both are zero

So substitute x = 0 and z = 0 in given equation

2(0) + 3y -6(0) = 30

0 + 3y + 0 = 30

3y = 30

y = 10

Thus the intercept is (0, 10, 0)

Thus at z - axis:

x and y are both zero

So substitute x = 0 and y = 0 in given equation

2(0) + 3(0) - 6z = 30

-6z = 30

z = -5

Thus the intercept is (0, 0, -5)

Thus, intercept of equation 2x + 3y - 6z = 30 is (15,0,0) ,(0,10,0) and (0,0,-5)