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The equation of a straight line containing the points (10,100) and (15
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30 Mar 2021, 05:34
30 Mar 2021, 05:34
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Question Stats:
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The equation of a straight line containing the points (10,100) and (15, 60) is
(A) \(y = –8x + 180\)
(B) \(y = 8x – 180\)
(C) \(y = \frac{x}{8} + 7.5\)
(D) \(y = –8x – 180\)
(E) \(y = –\frac{x}{8} + 22.5\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
(A) \(y = –8x + 180\)
(B) \(y = 8x – 180\)
(C) \(y = \frac{x}{8} + 7.5\)
(D) \(y = –8x – 180\)
(E) \(y = –\frac{x}{8} + 22.5\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Re: The equation of a straight line containing the points (10,100) and (15
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30 Mar 2021, 07:09
30 Mar 2021, 07:09
1
Carcass wrote:
The equation of a straight line containing the points (10,100) and (15, 60) is
(A) \(y = –8x + 180\)
(B) \(y = 8x – 180\)
(C) \(y = \frac{x}{8} + 7.5\)
(D) \(y = –8x – 180\)
(E) \(y = –\frac{x}{8} + 22.5\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
(A) \(y = –8x + 180\)
(B) \(y = 8x – 180\)
(C) \(y = \frac{x}{8} + 7.5\)
(D) \(y = –8x – 180\)
(E) \(y = –\frac{x}{8} + 22.5\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Notice that all of the answers are expressed in slope y-intercept form (y = mx + b, where m represents the line's slope and b represents the line's y-intercept)
We can use this to our advantage.
First let's sketch the two points and connect them with a line...
First notice that the slope of the line is NEGATIVE
So, we can ELIMINATE answer choices B and C, since those equations represent lines with POSITIVE slopes
Next notice that the y-intercept will be POSITIVE
So, we can ELIMINATE answer choice D, since that equation represents a line with a NEGATIVE y-intercept
We're left with answer choices A and E
The slope of answer choice A (y = –8x + 180) is -8, and the slope of answer choice E (y = –x/8 + 22.5) is -1/8
From our sketch, we can see that the line is quite steep, so we can ELIMINATE answer choice E, since a slope of -1/8 is not very steep.
Answer: A
General Discussion
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Status:Founder & Quant Trainer
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The equation of a straight line containing the points (10,100) and (15
[#permalink]
30 Mar 2021, 07:35
30 Mar 2021, 07:35
1
Carcass wrote:
The equation of a straight line containing the points (10,100) and (15, 60) is
(A) \(y = –8x + 180\)
(B) \(y = 8x – 180\)
(C) \(y = \frac{x}{8} + 7.5\)
(D) \(y = –8x – 180\)
(E) \(y = –\frac{x}{8} + 22.5\)
(A) \(y = –8x + 180\)
(B) \(y = 8x – 180\)
(C) \(y = \frac{x}{8} + 7.5\)
(D) \(y = –8x – 180\)
(E) \(y = –\frac{x}{8} + 22.5\)
Let the equation of the line be \(y = mx + c\)
Slope \((m) = \frac{100-60}{10-15} = -8\)
Now we can see that the line has a -ve slope (going down Left to Right), so the y-intercept value will be a +ve number greater than \(100\). Only option A satisfies this condition.
Hence, option A
