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GRE Math Challenge #133-In the rectangular coordinate system

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sandy
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GRE Math Challenge #133-In the rectangular coordinate system [#permalink] New post   Updated on: 20 Feb 2020, 16:12
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In the rectangular coordinate system, line k passes through the points (0,0) and (4,8); line m passes through the points (0,1) and (4,9).

Quantity A
Quantity B
The slope of line k
The slope of line m


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

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C

Originally posted by sandy on 15 May 2015, 11:36.
Last edited by Carcass on 20 Feb 2020, 16:12, edited 1 time in total.
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Re: GRE Math Challenge #133 [#permalink] New post   17 May 2015, 08:24
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sandy wrote:
In the rectangular coordinate system, line k passes through the points (0,0) and (4,8); line m passes through the points (0,1) and (4,9).

Quantity A: The slope of line k
Quantity B: The slope of line m


One approach is to sketch each line.
When we do so, we see that the two points for line m are each 1 UNIT ABOVE the two points for line k.
Image

Given this, the two lines must be PARALLEL, which means their slopes are EQUAL.

Answer:
Show: ::
C


Cheers,
Brent
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Re: GRE Math Challenge #133 [#permalink] New post   17 May 2015, 08:26
1
sandy wrote:
In the rectangular coordinate system, line k passes through the points (0,0) and (4,8); line m passes through the points (0,1) and (4,9).

Quantity A: The slope of line k
Quantity B: The slope of line m


Another option is to apply the slope formula.

Slope of line k = (8 - 0)/(4 - 0) = 8/4 = 2
Slope of line m = (9 - 1)/(4 - 0) = 8/4 = 2

Answer:
Show: ::
C


Cheers,
Brent
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Re: GRE Math Challenge #133-In the rectangular coordinate system [#permalink] New post   28 Sep 2020, 09:12
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Slope of a line connecting two points (\(x_1, y_1\)) and (\(x_2,y_2\)) in the xy-plane is given by \(\frac{(y_2-y_1) }{ (x_2-x_1)}\).

Applying the formula on the points through which line k is passing, slope of line k = \(\frac{8}{4}\) = 2

Similarly, slope of line m = \(\frac{8}{4}\) = 2

Both quantities are equal.
Correct answer is option C
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Re: GRE Math Challenge #133-In the rectangular coordinate system [#permalink]
28 Sep 2020, 09:12
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