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ln the coordinate plane, line k passes through the origin an
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06 Aug 2020, 10:45
06 Aug 2020, 10:45
Expert Reply
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Question Stats:
73% (01:16) correct
26% (02:47) wrong based on 15 sessions
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ln the coordinate plane, line k passes through the origin and has slope 2. lf points (3,y) and (x,4) are on line k, then x+y =
(A) 3.5
(B) 7
(C) 8
(D) 10
(E) 14
(A) 3.5
(B) 7
(C) 8
(D) 10
(E) 14
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Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: ln the coordinate plane, line k passes through the origin an
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06 Aug 2020, 12:06
06 Aug 2020, 12:06
1
Carcass wrote:
ln the coordinate plane, line k passes through the origin and has slope 2. lf points (3,y) and (x,4) are on line k, then x+y =
(A) 3.5
(B) 7
(C) 8
(D) 10
(E) 14
(A) 3.5
(B) 7
(C) 8
(D) 10
(E) 14
It often helps to write equations for lines in the form y = mx + b (this is called slope y-intercept form), where m = the slope of the line, and b = the y-intercept of the line.
The question tells us that the line has slope 2. So, m = 2
The question also tells us that the line passes through the origin (0,0). So, the y-intercept is 0, which means b = 0
So, the equation of the line is y = 2x + 0, or just y = 2x
If the point (3,y) is on the line, then its coordinates must satisfy the equation y = 2x
So, plug x=3 and y=y into the equation to get y = (2)(3) = 6
If the point (x,4) is on the line, then its coordinates must satisfy the equation y = 2x
So, plug x=x and y=4 into the equation to get 4 = 2x, which means x = 2
So, x + y = 2 + 6
= 8
= C
Cheers,
Brent
Re: ln the coordinate plane, line k passes through the origin an
[#permalink]
07 Aug 2020, 04:48
07 Aug 2020, 04:48
1
If line k goes through the origin and has slope 2, then its equations is
y=2x
Therefore
x+y=3x
If (x,4) and (3,y) are on the line then the slope calculated using these two points should be 2.
Therefore
(4-y)/(x-3) = 2
4-y=2x-6
10-y= 2x
10-2x= 2x (since y=2x)
10=4x
x=10/4= 2.5
3x= 7.5
So x+y= 7.5
I think the question is faulty.
y=2x
Therefore
x+y=3x
If (x,4) and (3,y) are on the line then the slope calculated using these two points should be 2.
Therefore
(4-y)/(x-3) = 2
4-y=2x-6
10-y= 2x
10-2x= 2x (since y=2x)
10=4x
x=10/4= 2.5
3x= 7.5
So x+y= 7.5
I think the question is faulty.
