To graph a plane, you will need at least two lines contained by the plane. Find and graph the equations of these two lines.
Practice makes perfect
We are asked to sketch the given plane.
x+2y-z=6
Before we do that, recall that two lines determine a plane. The lines contained in the plane can be found by substituting 0 for one of its variables. The resulting equation will represent a line. Let's first find the equation of the line that passes through x= 0.
Now that we know the equation of the line, we can use its intercepts to graph it. For the y-intercept, we will substitute z= 0. Similarly, for the z-intercept, we will substitute y= 0.
y-intercept
z-intercept
Substitute
2y- 0=6
2( 0)-z=6
Calculate
y= 3
z= -6
Point
( 0, 3, 0)
( 0, 0, -6)
Next, we can plot the intercepts on the coordinate space and draw the line through them.
Now we will find the equation of another line on the plane. This time, let's look for one that passes through y= 0.
