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# Which of the following is NOT an equation of one of the boundary lines

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Which of the following is NOT an equation of one of the boundary lines  [#permalink]

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12 May 2015, 10:27
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T6224.png [ 9.34 KiB | Viewed 1850 times ]
Which of the following is NOT an equation of one of the boundary lines of the shaded region in the figure above?

A. x=5
B. y=0
C. y=2−2x
D. x=0
E. y=2−x
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Re: Which of the following is NOT an equation of one of the boundary lines  [#permalink]

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12 May 2015, 21:30
Hi reto,

Looking at the answer choices, we can see that two of them are the equations for diagonal lines (Answers C and E). Since the drawing has just 1 diagonal line in it, one of these two equations IS the equation for that diagonal line while the other is NOT.

Based on the graph, we can see two obvious points on that line: (0,2) and (2,0). We can check these two points against the two equations. If either point does NOT fit the given equation, then that equation does not fit the drawing (and is the correct answer to this question).

When X = 2 is entered into Answer C, the result is 2-4 = -2; this is NOT a match (it's supposed to be 0)
When X = 2 is entered into Answer E, the result is 2-2 = 0; this IS a match.

Thus, the answer that is NOT in the drawing is....

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Re: Which of the following is NOT an equation of one of the boundary lines  [#permalink]

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12 May 2015, 21:45
Let's write down the equations of the line segments of the boundary lines

1. We know that x axis has the equation $$y = 0$$.Line segments lying on x -axis would have the same equation as $$y = 0$$

2. Similarly, y-axis has its equation as $$x = 0$$.Line segments lying on the y-axis would have the same equation as $$x = 0$$

3. A line segment passing through the point (5,0) and parallel to y-axis would have its equation written as $$x = 5$$

4. Similarly, a line segment passing through the point (0,5) and parallel to x-axis would have its line segment as $$y = 5$$

5. Now, we are left with just one line segment for which we know the two points it passes through. We can write the slope of the line segment as = $$\frac{(0-2)}{(2-0)} = -1$$. Thus we can write the equation as $$y = -x + c$$. Putting the coordinates (0,2) in the equation to find out the value of c, we get c = 2. So, equation of the line can be written as $$y = -x + 2$$

Hope it helps!

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Harsh
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Re: Which of the following is NOT an equation of one of the boundary lines  [#permalink]

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14 Jul 2016, 08:47
Which of the following is NOT an equation of one of the boundary lines of the shaded region in the figure above?
A. x=5 --> Top horizontal boundary of the figure
B. y=0 --> Left Vertical boundary of the figure
C. y=2−2x--> Hold it
D. x=0--> Bottom horizontal boundary of the figure
E. y=2−x--> The equation for the triangular cut

So Four equations have been accounted for OPTION A,B,D,E, The remaining OPTION C must be the answer.

reto wrote:
Attachment:
T6224.png
Which of the following is NOT an equation of one of the boundary lines of the shaded region in the figure above?

A. x=5
B. y=0
C. y=2−2x
D. x=0
E. y=2−x

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Re: Which of the following is NOT an equation of one of the boundary lines   [#permalink] 14 Jul 2016, 08:47