3.5 Graphing Linear Equations in Three Variables

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Presentation transcript:

3.5 Graphing Linear Equations in Three Variables OBJ: To Graph linear equations in three variables and evaluate linear functions in two variables 3.5 Graphing Linear Equations in Three Variables The 3D coordinate system: Tip: To PLOT find (x, y) first then move up or down z units

Ex 1: Plotting points in 3D a) Plot (3, -1, -5) b) Plot (-1, 3, 3)

A Linear Equation in 3 Variables: ax + by + cz = d Tip: To GRAPH, find the intercepts at x, y, and z by substituting zero

Ex 2: Graphing in 3D a) x – 2y + 2z = 6 Plane: like a slice or sliver that cuts through a 3D object a) x – 2y + 2z = 6

b) -15x + 10y – 6z = -30

Writing as a “Function”: solve for “z”, then replace with “f(x, y)” Ex 3: Write 3x – 12y + 5z = 30 as a function of x and y

Ex 4: Evaluate the function from Ex 3 when x = -2 and y = 2