sketch the plane x+2y-z=6.
if you need help,find a third line by letting z=0 and then graph the resulting equation in the xy plane
http://www.wolframalpha.com/input/?i=x%2B2y-z%3D6
To sketch the plane x + 2y - z = 6, we can follow the given steps:
1. Let's find a third line by letting z = 0. This means we set the value of z to 0 in the equation x + 2y - z = 6, resulting in x + 2y - 0 = 6, which simplifies to x + 2y = 6.
2. Now we have a linear equation in the xy-plane. Let's find the x and y-intercepts of the line x + 2y = 6.
- To find the x-intercept, we set y = 0 and solve for x: x + 2(0) = 6, which gives x = 6. So, the x-intercept is (6, 0).
- To find the y-intercept, we set x = 0 and solve for y: 0 + 2y = 6, which gives y = 3. So, the y-intercept is (0, 3).
3. Plot the x-intercept (6, 0) and the y-intercept (0, 3) on the xy-plane.
4. Draw a straight line passing through the x-intercept and y-intercept. This line represents the equation x + 2y = 6.
Note: The line you just drew on the xy-plane is the intersection of the plane x + 2y - z = 6 with the xy-plane when z = 0.