In this question, we investigate the graph (in three-dimensional space) of equations of the form ax+by+c= 0 (interpreted as ax+by+0z+c= 0). We consider the example 0.2x + 0.5y = 2. (a) Find a point (x, y, z) that satisfies the equation and for which x = 5. (b) What can be said about the points (x, y, z) that are obtained by changing only the z-coordinate from the point of part a? (c) What figure is determined by the points of part b in the three-dimensional (x, y, z)-space? What can you conclude about this figure and the graph of 0.2x +0.5y = 2? (d) Repeat parts a, b and c for a point (x, y, z) with x = 0. (e) What is the intersection of the graph of 0.2x +0.5y = 2 and the (x, y)-plane? (f) What is the (three-dimensional) graph of 0.2x + 0.5y = 2? (g) Does this graph determine a function?

In this question, we investigate the graph (in three-dimensional space) of equations of the form ax+by+c= 0 (interpreted as ax+by+0z+c= 0). We consider the example 0.2x + 0.5y = 2. (a) Find a point (x, y, z) that satisfies the equation and for which x = 5. (b) What can be said about the points (x, y, z) that are obtained by changing only the z-coordinate from the point of part a? (c) What figure is determined by the points of part b in the three-dimensional (x, y, z)-space? What can you conclude about this figure and the graph of 0.2x +0.5y = 2? (d) Repeat parts a, b and c for a point (x, y, z) with x = 0. (e) What is the intersection of the graph of 0.2x +0.5y = 2 and the (x, y)-plane? (f) What is the (three-dimensional) graph of 0.2x + 0.5y = 2? (g) Does this graph determine a function?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section: Chapter Questions

Problem 7DE

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