3'5: Graphing Linear Equations in Three Variables

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3.5 Graphing Linear Equations in Three Variables

• Goals
• Graph points and linear equations in 3 variables
  (Dimensions).
• Evaluate linear functions of 2 variables.

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3-Dimensions

• 3-Dimensional Coordinate System Coordinate
  Space
• Like a GPS, it gives location in 3 dimensions
• Latitude, Longitude, Elevation
• Ordered Triple a system of specifying a point in
  space using the form (x,y,z)

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Vocabulary contd

• Z-Axis The third axis in a
• 3-dimensional coordinate system

z-axis
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Key concepts
z
yz plane
-x
xy plane
-y
y
x
xz plane
-z
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A three dimensional Cartesian coordinate
system, with origin O and axis lines X, Y and Z,
oriented as shown by the arrows. The tic marks on
the axes are one length unit apart. The black dot
shows the point with coordinates X  2, Y  3,
and Z  4, or (2,3,4).
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Practice Problems

• 1. Graphing Points in 3-Dimensions
• a. A (-5,3,4)
• b. B (3, -4, -2)

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Linear Equations in Three Variables

• ax by cz d where a, b, and c are not all
  zero.
• Graph of a linear equation in 3 variables is a
  plane that contains all solutions.
• An ordered triple (x, y, z) is a solution of this
  equation if the equation is true when the values
  of x, y, and z are substituted into the equation

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Graphing a Linear Equation in 3 Variables

• Sketch the graph of 3x 2y 4z 12

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Evaluating a Function of 2 Variables

• Write the linear equation 3x 2y 4z 12 as a
  function of x and y.
• Evaluate the function when x 1 and y 3.

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Modeling a Real Life Situation

• LandscapingYou are planting a lawn and decide
  to use a mixture of two types of grass seed
  bluegrass and rye. The bluegrass costs 2 per
  pound, and the rye costs 1.50 per pound. To
  spread the seed you buy a spreader that costs
  35.
• Write a model for the total amount you will spend
  as a function of the number of pounds of
  bluegrass and rye.

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Homework

• Pg. 173 18-34 even, 38 - 40