Graphing Points and Linear Equations in Three Dimensions

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Presentation transcript:

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.

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!

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.

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.

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.

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

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.

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

Graphing Linear Equations in Three-Dimensions Sketch the graph of 9x + 3y – 6z = 18

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.