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Difficulty: 505-555 Level,   Coordinate Geometry,                     
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Re: In the coordinate plane, line k passes through the origin and has slop [#permalink]
VeritasKarishma
GMATD11
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

Show SpoilerMy Take
i used the method y2-y1/x1-x2 =2

4-y/x-3 =2

As line passes through origin y=2x
Upon solving both the equation i get x+y=7.5

OOps some different method required.

Guys is this the trick in Coordinate geometry that we generally have to put points in line and chk.instead of making equations with the points given.

Pls comment

@Fluke ---i searched this question but didn't found.

To find the line k, knowing a point through which it passes and the line's slope is sufficient.
Since it passes through origin and has slope 2, this is what it will look like:
Attachment:
Ques6.jpg
What is the meaning of slope? It means for every increase of 1 unit in x coordinate, y coordinate increases by 2 units. When x coordinate increases by 3 units (from the point (0,0)), y coordinate increases by 6 units. Hence the line passes through (3, 6). y must be 6.
When y coordinate increases by 4 units (from (0,0)), x coordinate must have increased by 2 units. The line must pass through (2, 4). x must be 2.
x+y = 2+6 = 8

Hi VeritasKarishma, I found this very interesting. Is there any article specifying this theory more in detail with a few examples? would greatly help in solidifying the learning!!
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Re: In the coordinate plane, line k passes through the origin and has slop [#permalink]
1
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Expert Reply
Kritisood
VeritasKarishma
GMATD11
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

Show SpoilerMy Take
i used the method y2-y1/x1-x2 =2

4-y/x-3 =2

As line passes through origin y=2x
Upon solving both the equation i get x+y=7.5

OOps some different method required.

Guys is this the trick in Coordinate geometry that we generally have to put points in line and chk.instead of making equations with the points given.

Pls comment

@Fluke ---i searched this question but didn't found.

To find the line k, knowing a point through which it passes and the line's slope is sufficient.
Since it passes through origin and has slope 2, this is what it will look like:
Attachment:
Ques6.jpg
What is the meaning of slope? It means for every increase of 1 unit in x coordinate, y coordinate increases by 2 units. When x coordinate increases by 3 units (from the point (0,0)), y coordinate increases by 6 units. Hence the line passes through (3, 6). y must be 6.
When y coordinate increases by 4 units (from (0,0)), x coordinate must have increased by 2 units. The line must pass through (2, 4). x must be 2.
x+y = 2+6 = 8

Hi VeritasKarishma, I found this very interesting. Is there any article specifying this theory more in detail with a few examples? would greatly help in solidifying the learning!!

Here are some posts that discuss lines, slopes and intercepts:
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/0 ... nd-points/
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/0 ... and-lines/
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2016/0 ... line-gmat/
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2016/1 ... line-gmat/
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2016/0 ... axis-gmat/
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Re: In the coordinate plane, line k passes through the origin and has slop [#permalink]
1
Kudos
Since
m=Slope=2
c=intersection on y-axis=0
y=2x

The line passes through (3,y)
y=2*3=6

The line also passes through (x,4)
4=2*x
x=2

x+y=2+6=8
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Re: In the coordinate plane, line k passes through the origin and has slop [#permalink]
Line k passes through the origin and has a slope of 2. The y-coordinate of (3, y) will be 6 units above the origin because the slope is 2. So, y = 6. The x-coordinate of (x, 4) will be 2 units to the right of the origin because the slope is 2. So, x = 2. Therefore, x + y = 2 + 6 = 8.

Hence, the answer is (C) 8.
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Re: In the coordinate plane, line k passes through the origin and has slop [#permalink]
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Re: In the coordinate plane, line k passes through the origin and has slop [#permalink]
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