1. 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

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

4. 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

5. b) -15x + 10y – 6z = -30

6. 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

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