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)