Chapter 1: Q. 129 (page 44)

Which of the following equations might have the graph shown? (More than one answer is possible.)
$(a) 2 x + 3 y = 6 (b) - 2 x + 3 y = 6 (c) 3 x - 4 y = - 12 (d) x - y = 1 (e) x - y = - 1 (f) y = 3 x - 5 (g) y = 2 x + 3 (h) y = - 3 x + 3$

Short Answer

Expert verified

The equation which describes the given line is

$(b) - 2 x + 3 y = 6 (c) 3 x - 4 y = - 12 (e) x - y = - 1 (g) y = 2 x + 3$

Step by step solution

Given information

We are given graph and several equations

Explanation for correct options

Consider the option

$b) - 2 x + 3 y = 6 y = \frac{2}{3} x + 2$

and

$c) 3 x - 4 y = - 12 4 y = 3 x + 12 y = \frac{3}{4} x + 3$

also

$e) x - y = - 1 y = x + 1$

Similarly

$g) y = 2 x + 3$

Each and every equation has positive y-intercept similarly from the graph we can say that the line has positive y-intercept

Consider the equations

$(a) 2 x + 3 y = 6 y = - \frac{2}{3} + 2 (d) x - y = 1 y = x - 1 (f) y = 3 x - 5 (h) y = - 3 x + 3$

In the equation a) and h) the slopes are negative where as in option d) and f) the y-intercept is negative hence this does not match the given graph of lines

Conclusion

The equations that can have the given graph as

$(b) - 2 x + 3 y = 6 (c) 3 x - 4 y = - 12 (e) x - y = - 1 (g) y = 2 x + 3$

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.

Which of the following equations might have the graph shown? (More than one answer is possible.)
$(a) 2 x + 3 y = 6 (b) - 2 x + 3 y = 6 (c) 3 x - 4 y = - 12 (d) x - y = 1 (e) x - y = - 1 (f) y = 3 x - 5 (g) y = 2 x + 3 (h) y = - 3 x + 3$

Short Answer

Step by step solution

Given information

Explanation for correct options

Consider the equations

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Geometry

Statistics

Discrete Mathematics

Mechanics Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

Which of the following equations might have the graph shown? (More than one answer is possible.)(a)2x+3y=6(b)-2x+3y=6(c)3x-4y=-12(d)x-y=1(e)x-y=-1(f)y=3x-5(g)y=2x+3(h)y=-3x+3

Short Answer

Step by step solution

Given information

Explanation for correct options

Consider the equations

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Geometry

Statistics

Discrete Mathematics

Mechanics Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

Which of the following equations might have the graph shown? (More than one answer is possible.)
$(a) 2 x + 3 y = 6 (b) - 2 x + 3 y = 6 (c) 3 x - 4 y = - 12 (d) x - y = 1 (e) x - y = - 1 (f) y = 3 x - 5 (g) y = 2 x + 3 (h) y = - 3 x + 3$