5 2 GRAPHING THREE VARIABLES An equation such

5. 2 GRAPHING THREE VARIABLES

An equation such as such that A, B, C, and D are not all zero is called linear a equation in three variables. We can regard an equation in one or two variables as an equation in three variables. Example: can be thought of as

In space, the graph of a linear equation in three variables is a plane. In order to graph a linear equation in three variables we find the x-, y , and z intercepts. zero a. To find the x-intercept, substitute and z and solve for x. zero b. To find the y-intercept, substitute and z zero and solve for y. c. To find the z-intercept, substitute and y and solve for z. for both y for both x

1. Sketch the graph of the equation x-intercept: y-intercept: z-intercept:

2. Sketch the graph of the equation x-intercept: y-intercept: z-intercept:

What did you find about the graph? The plane is parallel to the y-axis If the coefficient of a variable in an equation of a zero plane is , then the plane is parallel to the axis of that variable if the constant term is not zero.

3. Sketch the graph of the equation x-intercept: y-intercept: z-intercept:

What did you find about the graph? The plane contains the y-axis If the coefficient of a variable in an equation of a plane is zero , then the plane contains the axis of that variable if zero the constant term is.

4. Sketch the graph of the equation x-intercept: y-intercept: z-intercept:

What did you find about the graph? The plane is parallel to the x-axis and z-axis The plane is parallel to the xz-plane If the coefficients of two of the variables are zero, but the constant term is not zero, then theparallel graph is to the other twoparallel axes and to the plane of the other two variables.

Questions 5 -8: A. Name the x-, y , and z -intercepts. B. Determine whether or not the graph is parallel to or contains any of the coordinate axes, and if so, which one(s). C. Determine whether or not the graph is parallel to or coincides with one of the coordinate planes, and if so, which one. D. Graph.

5. 6. 7. 8.