Graphing points in three variables
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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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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


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


Pre-requisite Check

Graph an ordered pair (x,y)

  • (4,2)

  • (-2,3)

  • (-3,-1)

  • (1,-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


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)


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.


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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