Graph Plane x+2y+3z=0 | Math Tutorials

In summary, To graph the plane x + 2y + 3z = 0, you can draw the lines x + 2y = 0 on the x-y-plane and x + 3z = 0 on the x-z-plane, then connect them to form the plane. This approach is different from finding intercepts and may be easier.
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Hey, how would I graph the plane x + 2y + 3z = 0. We were taught to find the x,y and z intercepts and then connect them resulting in the plane. In the following equation, I get the points x=0,y=0 and z =0. I can see that the intercept approach doesn't work for this question. What else can I try?
 
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  • #2
hi baddin! :smile:
baddin said:
Hey, how would I graph the plane x + 2y + 3z = 0. … I can see that the intercept approach doesn't work for this question. What else can I try?

easy-peasy

draw the line x + 2y = 0 on the x-y-plane, and the line x + 3z = 0 on the x-z-plane, and join them :wink:
 
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  • #3
Thanks for your help, it looks correct! =D
 

1. What is the equation for the graph plane x+2y+3z=0?

The equation for the graph plane x+2y+3z=0 is a linear equation in three variables, x, y, and z. It represents a two-dimensional plane in a three-dimensional coordinate system.

2. How do you graph the plane x+2y+3z=0?

To graph the plane x+2y+3z=0, you can use the intercept method. This involves finding the x, y, and z intercepts of the plane and connecting them to form a triangle. Alternatively, you can use a three-dimensional graphing calculator or software to plot the plane.

3. What does the equation x+2y+3z=0 represent?

The equation x+2y+3z=0 represents a plane in three-dimensional space. It is a linear equation, meaning that it forms a straight line when graphed. The coefficients of the variables x, y, and z determine the slope of the plane.

4. How is the graph plane x+2y+3z=0 related to the Cartesian coordinate system?

The graph plane x+2y+3z=0 is related to the Cartesian coordinate system because it is a representation of a two-dimensional plane in a three-dimensional space. The Cartesian coordinate system is used to plot points and graph equations in three dimensions, including planes.

5. Can you solve for x, y, and z in the equation x+2y+3z=0?

Yes, the equation x+2y+3z=0 can be solved for x, y, and z. However, since it is a linear equation with three variables, there are infinitely many solutions. To solve for a specific value of x, y, or z, you would need additional information or constraints.

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