Chapter 1: Q. 132 (page 44)

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

Short Answer

Expert verified

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

Step by step solution

Given information

We are given a graph and equation

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

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

Conclusion

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

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

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

Short Answer

Step by step solution

Given information

Explanation for correct option

Explanation for other options

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Applied Mathematics

Logic and Functions

Decision Maths

Discrete Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

The figure shows the graph of two perpendicular lines. Which of the following pairs of equations might have such a graph?(a)y-2x=2y+2x=-1(b)y-2x=02y+x=0(c)2y-x=22y+x=-2(d)y-2x=2x+2y=-1(e)2x+y=-22y+x=-2

Short Answer

Step by step solution

Given information

Explanation for correct option

Explanation for other options

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Applied Mathematics

Logic and Functions

Decision Maths

Discrete Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

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