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3-5 Graphs in Three Dimensions

3-5 Graphs in Three Dimensions. Objective: To graph points and equations in three dimensions. Objectives. Graphing Points in Three Dimensions Graphing Equations in Three Dimensions. Vocabulary. You’ve learned to graph on an xy -coordinate plane using ordered pairs.

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3-5 Graphs in Three Dimensions

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  1. 3-5 Graphs in Three Dimensions Objective: To graph points and equations in three dimensions

  2. Objectives Graphing Points in Three Dimensions Graphing Equations in Three Dimensions

  3. Vocabulary You’ve learned to graph on an xy-coordinate plane using ordered pairs. Adding a third axis, the z-axis, to the xy-coordinate plane creates coordinate space. In coordinate space, you graph points using ordered triples of the form (x, y, z)

  4. From the origin, move back 3 units, From the origin, move back 3 units, and down 4 units. right 3 units left 4 units and up 2 units. Graphing a Coordinate Space Graph each point in the coordinate space. a. (–3, 3, –4) Sketch the axes. b. (–3, –4, 2) Sketch the axes.

  5. A(–3, –3, 3), B(–3, 3, 3), C(3, 3, 3), D(3, –3, 3), E(3, –3, –3), F(3, 3, –3), G(–3, 3, –3), H(–3, –3, –3) Real World Example In the diagram, the origin is at the center of a cube that has edges 6 units long. The x-, y-, and z-axes are perpendicular to the faces of the cube. Give the coordinates of the corners of the cube.

  6. Sketching a Plane Sketch the graph of –3x – 2y + z = 6. Step 1:  Find the intercepts. –3x– 2y + z = 6 –3x – 2(0) + (0) = 6 To find the x-intercept, substitute 0 for y and z. –3x = 6 x = –2 The x-intercept is –2. –3(0) – 2y + (0) = 6 To find the y-intercept, substitute 0 for x and z. –2y = 6 y = –3 The y-intercept is –3. –3(0) – 2(0) + z = 6 To find the z-intercept, substitute 0 for x and y. z = 6 The z-intercept is 6.

  7. Step 3: Draw the traces. Shade the plane. Continued (continued) Step 2: Graph the intercepts. Each point on the plane represents a solution to –3x – 2y + z = 6.

  8. Homework Pg 149 # 5,6,13,14,15,16,17,18,19,20

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