Since the given equation has three variables, its graph is a plane. To draw the graph, first find and graph the equations of two lines on the plane.
Practice makes perfect
First, notice that the graph of the equation is a plane. Recall that two lines determine a plane. Therefore we need to find two distinct lines that lie on our plane in order to graph it.
6x+6y-12z=36
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
6y-12( 0)=36
6( 0)-12z=36
Calculate
y= 6
z= -3
Point
( 0, 6, 0)
( 0, 0, -3)
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 the line that passes through y= 0.
