Given the equation 2x-3y+4z=12, to calculate the intercepts we proceed as follows: x-intercept: To get x-intercept we let y=0 and z=0. The substitute these values in our equations follows: 2x+3(0)+4(0)=12 2x=12 hence: x=12/2 x=6 therefore the x-intercept will be at point (6,0,0)
y-intercept: To calculate for y-intercept we let x=0 and z=0 and substitute the values in the equation, here we shall have: 2(0)-3y+4(0)=12 solving for y we get: -3y=12 hence: y=12/(-3) y=-4 therefore the y-intercept is at point (0,-4,0)
z-intercept: To get the z-intercept we let x=0 and y=0, the we substitute the values in the equation as follows: 2(0)-3(0)+4z=12 solving for z we get: 4z=12 z=12/4 z=3 hence the z-intercept is at (0,0,3)