GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
In the x-y coordinate plane, line k passes through
[#permalink]
16 Oct 2018, 04:55
16 Oct 2018, 04:55
1
1
8
Bookmarks
00:00
Question Stats:
37% (01:52) correct
62% (01:44) wrong based on 110 sessions
Hide Show timer Statistics
In the x-y coordinate plane, line k passes through the point (5, -4) and has a negative x-intercept. Which of the following COULD be the equation of line k?
i) y = -0.4x - 2
ii) y = 2 - 1.2x
iii) y = -0.7x - 1.5
A) i only
B) ii only
C) iii only
D) i & ii only
E) i & iii only
i) y = -0.4x - 2
ii) y = 2 - 1.2x
iii) y = -0.7x - 1.5
A) i only
B) ii only
C) iii only
D) i & ii only
E) i & iii only
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: In the x-y coordinate plane, line k passes through
[#permalink]
18 Oct 2018, 09:35
18 Oct 2018, 09:35
3
GreenlightTestPrep wrote:
In the x-y coordinate plane, line k passes through the point (5, -4) and has a negative x-intercept. Which of the following COULD be the equation of line k?
i) y = -0.4x - 2
ii) y = 2 - 1.2x
iii) y = -0.7x - 1.5
A) i only
B) ii only
C) iii only
D) i & ii only
E) i & iii only
i) y = -0.4x - 2
ii) y = 2 - 1.2x
iii) y = -0.7x - 1.5
A) i only
B) ii only
C) iii only
D) i & ii only
E) i & iii only
Notice that, if the line passes through the origin, then the line has slope -4/5 (aka a slope of -0.8), but the line will not have a negative x-intercept
Notice that, if the line passes through the (0,4), then the line will have slope 0, BUT the line will not have a negative x-intercept. See below.
So, if the slope of the line is BETWEEN 0 and -0.8, then the line will have a negative x-intercept
Check the 3 statements:
i) y = -0.4x - 2
The slope = -0.4, which is BETWEEN 0 and -0.8. KEEP i for now
ii) y = 2 - 1.2x
Rewrite as: y = -1.2 + 2.
The slope = -1.2, which is NOT BETWEEN 0 and -0.8. So, ii cannot be true
iii) y = -0.7x - 1.5
The slope = -0.7, which is BETWEEN 0 and -0.8. KEEP iii for now
So far, i and iii COULD both be true.
However, in order for the point (5, -4) to be ON line k, its x and y coordinates must satisfy the equation of the line.
So, let's check i and iii
i) y = -0.4x - 2
Plug in x = 5 and y = -4 to get: -4 = -0.4(5) - 2 = -2 - 2 = -4
PERFECT!
So, i is true
iii) y = -0.7x - 1.5
Plug in x = 5 and y = -4 to get: -4 = -0.7(5) - 1.5 = -3.5 - 1.5 = -5
NO GOOD
So, iii is not true
Answer: A
Cheers,
Brent
General Discussion
Re: In the x-y coordinate plane, line k passes through
[#permalink]
16 Oct 2018, 17:29
16 Oct 2018, 17:29
1
Expert Reply
GreenlightTestPrep wrote:
In the x-y coordinate plane, line k passes through the point (5, -4) and has a negative x-intercept. Which of the following COULD be the equation of line k?
i) y = -0.4x - 2
ii) y = 2 - 1.2x
iii) y = -0.7x - 1.5
A) i only
B) ii only
C) iii only
D) i & ii only
E) i & iii only
i) y = -0.4x - 2
ii) y = 2 - 1.2x
iii) y = -0.7x - 1.5
A) i only
B) ii only
C) iii only
D) i & ii only
E) i & iii only
Two points one should note..
1) the point is in IV quadrant.
2) thereafter it crosses the III quadrant and moves to touch X axis in left of origin.
So it crosses y axis below the origin, so intercept would be negative..
(ii) is positive when xis 0..y=2-1.2*0=2, so not possible
Remaining two are ok on this aspect
Now (5,-4) should satisfy the equations..
(i) y=-0.4x-2....-4=-0.4*5-2=-2-2=-4..yes
(iii) y=-0.7x-1.5.....-4=-0.7*5-1.5=-3.5-1.5=-5...no
So only (i)
A
