3.5 Graphs in Three Dimensions
October 21, 2008
3­5 Graphs in Three Dimensions
Objectives
Graph points and equations in three dimensions.
Oct 18­5:12 AM
1
3.5 Graphs in Three Dimensions
October 21, 2008
Check Skills You'll Need
Find the x- and y-intercepts of the graph of each linear equation.
1. y = 2x + 6
2. 2x + 9y = 36
3. 3x - 8y = -24
Graph each linear equation.
4. y = 3x
5. y = -2x + 4
6. -3x - 2y = 7
Oct 18­5:22 AM
2
3.5 Graphs in Three Dimensions
October 21, 2008
A three-dimensional coordinate system allows you to graph points in space.
Points are represented by
ordered triples.
(3, 5, 4)
The point (3, 5, 4) is
3 units forward
5 units right, and
4 units up.
Oct 18­5:45 AM
3
3.5 Graphs in Three Dimensions
October 21, 2008
You can turn regular graph paper into three dimensional graph paper!
z
Step 1: Make your vertical (z) and horizontal (y) axes.
y
x
Step 2: Make your diagonal (x) axis.
Notice where the positive quadrant lies.
Oct 18­6:12 AM
4
3.5 Graphs in Three Dimensions
October 21, 2008
You can turn regular graph paper into three dimensional graph paper!
z
y
x
Some people just use these axes on their graph paper.
Notice where the positive quadrant lies.
Oct 18­6:12 AM
5
3.5 Graphs in Three Dimensions
October 21, 2008
Graph the following points:
z
1. (0, 3, ­2)
2. (­2, ­1, ­3)
3. (0, ­4, ­2)
y
4. (­1, 1, 3)
5. (3, ­5, ­2)
6. (3, 3, ­3)
x
Oct 18­6:14 AM
6
3.5 Graphs in Three Dimensions
October 21, 2008
Oct 18­3:25 PM
7
3.5 Graphs in Three Dimensions
October 21, 2008
Oct 18­3:25 PM
8
3.5 Graphs in Three Dimensions
October 21, 2008
Oct 18­3:41 PM
9
3.5 Graphs in Three Dimensions
October 21, 2008
Oct 18­3:27 PM
10
3.5 Graphs in Three Dimensions
October 21, 2008
Page: 149­150
#'s: 19­26, 53­55
Oct 18­3:42 PM
11