Chapter 1: Q. 130 (page 44)

Which of the following equations might have the graph shown? (More than one answer is possible.)
$(a) 2 x + 3 y = 6 (b) 2 x - 3 y = 6 (c) 3 x + 4 y = 12 (d) x - y = 1 (e) x - y = - 1 (f) y = - 2 x - 1 (g) y = - \frac{1}{2} x + 10 (h) y = x + 4$

Short Answer

Expert verified

The following equations describes the given line

$(a) 2 x + 3 y = 6 (c) 3 x + 4 y = 12 (g) y = - \frac{1}{2} x + 10$

Step by step solution

Given information

We are given graph and several equations.

Step 2: Explanation for correct options

The lines shown in the graph has positive y-intercept and also the slope of the line is negative

Consider the equation

$(a) 2 x + 3 y = 6 y = - \frac{2}{3} + 6 (c) 3 x + 4 y = 12 y = - \frac{3}{4} x + 3 (g) y = - \frac{1}{2} x + 10$

In all the above options the slope is negative and y-intercept is positive

Hence the graph can describe the given lines

Explanation for other options

Consider the equations

$(b) 2 x - 3 y = 6 y = \frac{2}{3} x + 2 (d) x - y = 1 y = x - 1 (e) x - y = - 1 y = x + 1 (f) y = - 2 x - 1 (h) y = x + 4$

From the above options options b) ,d) ,e),h) have positive slope

And option f) has negative y-intercept

Hence the graph can not be described by these lines

Conclusion

The graph can describe the given lines

$(a) 2 x + 3 y = 6 (c) 3 x + 4 y = 12 (g) y = - \frac{1}{2} x + 10$

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Which of the following equations might have the graph shown? (More than one answer is possible.)
$(a) 2 x + 3 y = 6 (b) 2 x - 3 y = 6 (c) 3 x + 4 y = 12 (d) x - y = 1 (e) x - y = - 1 (f) y = - 2 x - 1 (g) y = - \frac{1}{2} x + 10 (h) y = x + 4$

Short Answer

Step by step solution

Given information

Step 2: Explanation for correct options

Explanation for other options

Conclusion

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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=-2x-1(g)y=-12x+10(h)y=x+4

Short Answer

Step by step solution

Given information

Step 2: Explanation for correct options

Explanation for other options

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Geometry

Discrete Mathematics

Decision Maths

Theoretical and Mathematical Physics

Calculus

Study anywhere. Anytime. Across all devices.

Which of the following equations might have the graph shown? (More than one answer is possible.)
$(a) 2 x + 3 y = 6 (b) 2 x - 3 y = 6 (c) 3 x + 4 y = 12 (d) x - y = 1 (e) x - y = - 1 (f) y = - 2 x - 1 (g) y = - \frac{1}{2} x + 10 (h) y = x + 4$