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Equations for Surfaces

Equations for Surfaces. Integrated Math 4 Mrs. Tyrpak. Ax + By + Cz = D. This equation in three-space is analogous to the equation Ax + By = C in two – space. The graph of Ax + By = C is _________ so The graph of Ax+By+Cz =D is _______. Consider 2x + 4y +3z = 12.

matthew-thornton
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Equations for Surfaces

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  1. Equations for Surfaces Integrated Math 4 Mrs. Tyrpak

  2. Ax + By + Cz = D This equation in three-space is analogous to the equation Ax + By = C in two – space. The graph of Ax + By = C is _________ so The graph of Ax+By+Cz=D is _______

  3. Consider 2x + 4y +3z = 12 Using our reasoning from two-space let’s find what points the surface intersects the x, y, and z axes.

  4. Traces Traces are cross sections of the surface formed by the intersection of the coordinate planes. For example, since every point on the xy-plane has z = 0, the trace in the xy-plane is found by setting z = 0.

  5. Finding Traces Find the traces of 2x + 4y +3z = 12 in the xy-plane, the yz-plane, and the xz-plane. Based on this information, what does this tell us about the surface?

  6. Intersections In Two-Space: 2 lines can intersect in 0 points, 1 point or infinitely many points. In Three-Space:

  7. Visuals

  8. Practice: 2x - y + 3z = 6 Sketch a graph using the intercepts, and find the traces in each coordinate plane.

  9. You know what I’m going to say! Awesome job!! Don’t forget to complete your extension and enrichment worksheets before you move on. Remember you are a mathematician 

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