What are the intercepts of 2x + 3y - 6z = 30? a: (15, 0, 0), (0, 10, 0), (0, 0, 5) b: (15, 0, 0), (0, -10, 0), (0, 0, 5) c: (15, 0, 0), (0, -10, 0), (0, 0, -5) d: (15, 0, 0), (0, 10, 0), (0, 0, -5)

Option (d) is correct.

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

Step-by-step explanation:

given : The equation  2x + 3y - 6z = 30

We have to find the intercept.

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, put y = z = 0

we get,

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

2x = 30

x = 15

at y- axis

x and z both are zero .

So, put x = z = 0

we get,

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

3y = 30

y = 10

at z- axis

y and x both are zero .

So, put y = x = 0

we get,

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

-6z = 30

z= -5

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

the least common denominator is 40