Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

The figure shows the graph of two perpendicular lines. Which of the following pairs of equations might have such a graph?
$(a) y - 2 x = 2 y + 2 x = - 1 (b) y - 2 x = 0 2 y + x = 0 (c) 2 y - x = 2 2 y + x = - 2 (d) y - 2 x = 2 x + 2 y = - 1 (e) 2 x + y = - 2 2 y + x = - 2$

Equation $(d) y - 2 x = 2 x + 2 y = - 1$ might have such graph

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given information

We are given a graph and equation

Step 2: Explanation for correct option

Consider the option $(d) y - 2 x = 2 x + 2 y = - 1$

Simplifying the equation and writing it in slope intercept form we get

$y = 2 x + 2 y = - \frac{1}{2} x - \frac{1}{2}$

On multiplying the slope we get $- 1$

Hence the lines are perpendicular

Step 3: Explanation for other options

Consider the equations

$(a) y - 2 x = 2 y + 2 x = - 1 (b) y - 2 x = 0 2 y + x = 0 (c) 2 y - x = 2 2 y + x = - 2 (e) 2 x + y = - 2 2 y + x = - 2$

On simplifying the equation we get

$(a) y = 2 x + 2 y = - 2 x - 1 (b) y = 2 x y = - \frac{1}{2} x (c) y = \frac{x}{2} + 1 y = - \frac{x}{2} - 1 (e) y = - 2 x - 2 y = - \frac{x}{2} - 1$

On multiplying the slopes of equation of lines in options a) ,c) ,d) we do not get $- 1$

And for option b) on multiplying the slopes we do get $- 1$ but the lines passes through the origin hence the given graph cannot be described by the lines

Step 4: Conclusion

The equation $(d) y - 2 x = 2 x + 2 y = - 1$ might have such graph.

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Precalculus Enhanced with Graphing Utilities

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Short Answer

The figure shows the graph of two perpendicular lines. Which of the following pairs of equations might have such a graph?
$(a) y - 2 x = 2 y + 2 x = - 1 (b) y - 2 x = 0 2 y + x = 0 (c) 2 y - x = 2 2 y + x = - 2 (d) y - 2 x = 2 x + 2 y = - 1 (e) 2 x + y = - 2 2 y + x = - 2$

Step by Step Solution

Step 1: Given information

Step 2: Explanation for correct option

Step 3: Explanation for other options

Step 4: Conclusion

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Precalculus Enhanced with Graphing Utilities

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Short Answer

The figure shows the graph of two perpendicular lines. Which of the following pairs of equations might have such a graph?(a) y - 2x = 2 y + 2x = -1(b) y - 2x = 0 2y + x = 0 (c) 2y - x = 2 2y + x = -2 (d) y - 2x = 2 x + 2y = -1 (e) 2x + y = -2 2y + x = -2

Step by Step Solution

Step 1: Given information

Step 2: Explanation for correct option

Step 3: Explanation for other options

Step 4: Conclusion

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The figure shows the graph of two perpendicular lines. Which of the following pairs of equations might have such a graph?
$(a) y - 2 x = 2 y + 2 x = - 1 (b) y - 2 x = 0 2 y + x = 0 (c) 2 y - x = 2 2 y + x = - 2 (d) y - 2 x = 2 x + 2 y = - 1 (e) 2 x + y = - 2 2 y + x = - 2$