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The slope of line K

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The slope of line K [#permalink] New post 01 Feb 2017, 13:36
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Attachment:
GRE - powerprep The slope of line K.jpg
GRE - powerprep The slope of line K.jpg [ 9.23 KiB | Viewed 991 times ]


Quantity A
Quantity B
The slope of line K
1


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: The slope of line K [#permalink] New post 06 Feb 2017, 10:22
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Explanation

On the GRE, coordinate geometry figures ARE drawn to scale, so we can determine from the graphic that line k runs through the origin (0, 0). It is impossible to determine the slope of line k, however, because we only have one point on that line (0, 0). Instead, create a line (line l) that runs through the point (3, 4) and the origin (0, 0) to find it's slope:

Image


The slope of line l can be found by computing the rise (4) over the run (3):

Slope of line l= 4/3

As you know, 4/3 is greater than 1, and since line k has a slope that is even steeper than 4/3, you know it is also greater than 1.

For comparison's sake, a line with a slope of 1 would run through the 3 points below line l.

Hence option A is correct.

[Reveal] Spoiler: Img
Attachment:
di.jpg
di.jpg [ 13.73 KiB | Viewed 7510 times ]

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Re: The slope of line k [#permalink] New post 07 Mar 2018, 15:24
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It's useful to know that a slope of 1 will produce a line that goes at a 45 degree angle. It will also pass through a series of points in which x and y are the same, i.e. (4, 4), (27, 27), (-11, -11), etc.

The picture shows a slope that appears more steep than a 45 degree angle. Verifying that it is in fact steeper, we can compare the line with the point (3, 4). A line drawn through the origin to the point (3, 4) would go upwards more than it went rightwards, so would be steeper than a slope of 1. This slope is steeper than that. Thus, the answer is A.
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Re: The slope of line K [#permalink] New post 15 Feb 2019, 11:29
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Carcass wrote:



Attachment:
GRE - powerprep The slope of line K.jpg


Quantity A
Quantity B
The slope of line K
1


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


Slope = rise/run

So, if we draw a line from the origin (0,0) and the point (3,4)...
Image
...we can see that the slope of that line = 4/3


From our diagram...
Image
...we can see that the slope of line k is STEEPER than the slope of our red line
So, the slope of k must be greater than 4/3

We get:
QUANTITY A: Some number greater than 4/3
QUANTITY B: 1

Answer: A

Cheers,
Brent
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Re: The slope of line K   [#permalink] 15 Feb 2019, 11:29
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