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Graphing Points in Three Variables

Graphing Points in Three Variables. AII, 2.0: Students solve systems of linear equations and inequalities (in two or three variables) by substitution, with graphs, or with matrices.

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Graphing Points in Three Variables

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  1. Graphing Points in Three Variables AII, 2.0: Students solve systems of linear equations and inequalities (in two or three variables) by substitution, with graphs, or with matrices. LA, 6.0: Students demonstrate an understanding that linear systems are inconsistent (have no solutions), have exactly one solution, or have infinitely many solutions

  2. Graphing Points in Three Variables Objectives Key Words Three-dimensional coordinate system Z-axis Ordered triple Origin (0,0,0) Octanes xz-plane yz-plane xy-plane • Describe the location of each point in relation to the origin • Write the coordinates of each point • Plot points in three dimensions

  3. Pre-requisite Check Graph an ordered pair (x,y) • (4,2) • (-2,3) • (-3,-1) • (1,-4)

  4. Describe the location of each point in relation to the origin For the x-axis: Positive Direction: Move Forward Like jumping out of the paper Negative Direction: Moving Back Like going behind the paper For the y-axis: Positive Direction: Moving Right Negative Direction: Moving Left For the z-axis: Positive Direction: Moving Up Negative Direction: Moving Down

  5. Write the coordinates of each point (1,-4,3) It takes a few steps to solve these types of problems: What direction is it moving on the x-axis? How much? This is you x value. What direction is it moving on the y-axis? How much? This is you y value. What direction is it moving on the z-axis? How much? This is you z value. Write the ordered triple (x,y,z)

  6. Plot points in three dimensions Example: Mark the x value direction Mark the y value direction Find the point of intersection Travel the z value direction (upward or downward) Plot the point.

  7. Conclusions Summary Assignment To be completed in class Worksheet: Points in Three Dimensions • What are the directions you travel to plot the points of an ordered triple where the x, y, and z values are positive? • For the x, forward • For the y, right • For the z, upward

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