Answer: (3, 0, 0), (0, 2, 0), (0, 0, 6)
Explanation:
The x intercept is the point where the graph intersects the x axis.
To find this, we single out x.
4x = 12 - 6y - 2z
x = 3 - 3y/2 - z/2
The constant in the graph is 3. Therefore the x intercept is 3, where z and y are 0. ( y and z have to be 0 for the graph to intersect the x axis) The x intercept is (3,0,0)
Note that we gained this value by dividing the constant in the original graph (in this case 12), by the coefficient of the variable whose intercept we needed to find.
So we can find the y intercept by dividing 12 by the y coefficient, 6. Therefore the y intercept is (0,2,0)
Similarly the z intercept is found by dividing 12 by the z coefficient, 2.
Therefore, the z intercept is (0,0,6)
So the intercepts of your graph are (3,0,0), (0,2,0),(0,0,6)
Hope i helped you!!! :)