3-variable linear equations (part 1) | Summary and Q&A

TL;DR

Graphing three-variable linear equations involves visualizing planes in three dimensions.

Key Insights

• ✈️ Three-variable linear equations represent planes in three dimensions.
• 🤪 The x-intercept, y-intercept, and z-intercept help in graphing the planes.
• 🫥 The intersection of two equations with three variables is a line, while the intersection of three equations is a unique point.

Transcript

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Questions & Answers

Q: How do you graph a three-variable linear equation in three dimensions?

To graph a three-variable linear equation, you can represent it as a plane in three dimensions by identifying the x-intercept, y-intercept, and z-intercept. These intercepts help visualize the plane on a graph.

Q: What does the intersection of two equations with three variables represent?

The intersection of two equations with three variables represents a line in three dimensions. This line is the common solution to both equations.

Q: What happens when a third equation is added to two equations with three variables?

Adding a third equation to two equations with three variables results in the intersection of three planes at a unique point. This point represents the solution to all three equations.

Q: How can the graph of a three-variable linear equation be visualized on a two-dimensional surface?

Graphing a three-variable linear equation on a two-dimensional surface can be challenging. However, by drawing the intercepts and connecting them, one can get an idea of the shape of the plane. It is easier to visualize on a computer with the ability to rotate the graph.

Summary & Key Takeaways

• Graphing three-variable linear equations involves representing a plane in three dimensions.

• The x-intercept, y-intercept, and z-intercept can be used to draw the plane on a graph.

• When two equations with three variables are graphed, the intersection is a line. Adding a third equation will result in a unique point of intersection.