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In the coordinate plane, line k passes through the origin and has slop

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Difficulty: 505-555 Levelx   Coordinate Geometryx                     
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CatchTwentyTwo
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Re: In the coordinate plane, line k passes through the origin and has slop [#permalink] New post   20 Nov 2018, 18:11
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Since k passes through the origin (0,0), the y-intercept will be 0.

\(y = mx + b\)
\(0 = m0 + b\)
\(0 = b\)

Also, since the slope is 2, our equation becomes:

\(y = mx + b\)
\(y = 2x + 0\)

Finally, x and y are found by plugging in the values for each point then solving for the unknown variable.

\((3,y)\)
\(y = 2(3) + 0\)
\(y = 6\)

\((x,4)\)
\(4 = 2x + 0\)
\(2 = x\)
\(x+y\)
\(2+6 = 8\)
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Re: In the coordinate plane, line k passes through the origin and has slop [#permalink] New post   26 Oct 2019, 06:20
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Hi EMPOWERgmatRichC
Quote:
Y = 2X

(3, B) and (A, 4) are on the line. What is the value of A+B?


Could you please help me clear my small doubt?

So if I am getting this correctly, it's not true that a line passing through the origin will not always have a eq of typical y=x (for + slope) and y=-x (for - slope) it can be y= 2x as well?

Thank you,
Dablu
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Re: In the coordinate plane, line k passes through the origin and has slop [#permalink] New post   26 Oct 2019, 19:21
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Hi gurudabl,

When a line is written in slope-intercept 'format' (Y = MX + B) if there is NO "B" value, then the line moves through the Origin (re: the point 0,0). The slope (re: the "M") has no impact on that, meaning that as long as B=0, then ANY value of M will give us a line that moves through the Origin. Try graphing any of the following lines and you'll see:

Y = X
Y= 2X
Y = 100X
Y = (-1)X
Y = (-99)X
Y = .00005X
etc.

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Re: In the coordinate plane, line k passes through the origin and has slop [#permalink] New post   05 Mar 2020, 09:02
VeritasKarishma wrote:
GMATD11 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

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] New post   05 Mar 2020, 21:09
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Kritisood wrote:
VeritasKarishma wrote:
GMATD11 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

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] New post   20 Jun 2021, 08:20
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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] New post   03 Jun 2023, 01:41
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]
03 Jun 2023, 01:41
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