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**Graphing Points and Linear Equations in Three Dimensions**

Objective: When I leave class today, I should be able to: (1) Graph points and linear equations in three dimensions.

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**How to Plot Points in Three Dimensions**

Plotting points in three dimensions is very similar to plotting in two, with just one difference; instead of having two axes, you have three!

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**Know the axes. The axes in three dimensions are x, y, and z**

Know the axes. The axes in three dimensions are x, y, and z. The coordinate system looks like this with the x-axis pointing toward you.

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We normally use the 'right-hand orientation' for the 3 axes, with the the positive x-axis pointing in the direction of the first finger of our right hand, the positive y-axis pointing in the direction of our second finger and the positive z-axis pointing up in the direction of our thumb.

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**Know how to read the ordered triples**

Know how to read the ordered triples. The form for ordered triples is (x,y,z) so the point (3,2,4) would mean 3 units along the x-axis, 2 along the y-axis, and 4 along the z axis.

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**In 3-dimensional space, the point (2, 3, 5) is graphed as follows:**

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**Graphing Linear Equations in Three-Dimensions**

Recall that the graph of a linear equation in two dimensions is a straight line. In three dimensional space, the graph of a linear equation is a plane. Because a plane is defined in three points, you can graph linear equations in three dimensions by finding the three intercepts.

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**Graphing Linear Equations in Three-Dimensions**

A point on the x-axis has the form (x, 0, 0). A point on the y-axis has the form (0, y, 0). A point on the z-axis has the form (0, 0, z). Sketch the graph of 2x - y + 4z = 8

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**Graphing Linear Equations in Three-Dimensions**

Sketch the graph of 9x + 3y – 6z = 18

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**Model a Real-Life Situation**

At an aquarium, you can buy pens for $3 each and patches for $4 each. Admission to the aquarium costs $12. a. Write a linear model for the total cost you will spend for admission and souvenirs. b. Evaluate the model for the total amount you will spend for 2 pens and 3 patches.

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