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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
In the x-y coordinate plane, line k passes through
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16 Oct 2018, 04:55
16 Oct 2018, 04:55
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Question Stats:
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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
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18 Oct 2018, 09:35
18 Oct 2018, 09:35
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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
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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
