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# Line k is in the rectangular coordinate system. If the x-intercept of

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Math Expert
Joined: 02 Sep 2009
Posts: 43896
Line k is in the rectangular coordinate system. If the x-intercept of [#permalink]

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26 Mar 2015, 03:31
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Difficulty:

25% (medium)

Question Stats:

74% (01:10) correct 26% (01:25) wrong based on 183 sessions

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Line k is in the rectangular coordinate system. If the x-intercept of k is -2, and the y-intercept is 3, which of the following is an equation of line k?

A. -3x + 2y = 6
B. 3x + 2y = -6
C. 3x - 2y = 6
D. 2x - 3y = 6
E. -2x - 3y = 6

Kudos for a correct solution.
[Reveal] Spoiler: OA

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Re: Line k is in the rectangular coordinate system. If the x-intercept of [#permalink]

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26 Mar 2015, 06:20
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Bunuel wrote:
Line k is in the rectangular coordinate system. If the x-intercept of k is -2, and the y-intercept is 3, which of the following is an equation of line k?

A. -3x + 2y = 6
B. 3x + 2y = -6
C. 3x - 2y = 6
D. 2x - 3y = 6
E. -2x - 3y = 6

Kudos for a correct solution.

y intercept is 3
y=mx+3 (where x is the independent variable; m is the slope; 3 is the y intercept of k)

(y-3)/m=x

Therefore,
-3/m=-2 (Since the constant is the x intercept)
m=3/2

Putting it in the initial equation
y=mx+c
y=3/2x+3
2y-3x=6

Senior Manager
Joined: 02 Mar 2012
Posts: 356
Schools: Schulich '16
Re: Line k is in the rectangular coordinate system. If the x-intercept of [#permalink]

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26 Mar 2015, 06:32
1
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A

eq of line is y=mx+c

we have two points (-2,0) and (0,3)

so slope is 3/2 and by substituing any point in the eq with the slope we can find out the value of c which comes out to be 6

so equation is 2y-3x=6
Intern
Joined: 20 Mar 2015
Posts: 18
Location: Italy
GMAT 1: 670 Q48 V34
GPA: 3.7
Re: Line k is in the rectangular coordinate system. If the x-intercept of [#permalink]

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27 Mar 2015, 01:13
2
KUDOS
For $$(-2,0)$$

A. -3(-2) + 2(0) = 6 True
B. 3(-2) + 2(0) = -6 True
C. 3(-2) - 2(0) = 6 Exclude
D. 2(-2) - 3(0) = 6 Exclude
E. -2(-2) - 3(0) = 6 Exclude

For $$(0,3)$$

A. -3(0) + 2(3) = 6 True
B. 3(0) + 2(3) = -6 Exclude

Director
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Joined: 03 Oct 2013
Posts: 518
Location: India
GMAT 1: 780 Q51 V46
Re: Line k is in the rectangular coordinate system. If the x-intercept of [#permalink]

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27 Mar 2015, 02:50
1
KUDOS
Hi all,
This question can be solved in much simpler way.
To find the x intercept
Put y=0 in the equation of the line.
To find the y-intercept
Put x=0 in the equation of the line.
So
Sub x=0 in the answer choices check whether you are getting y=3.
A. -3x + 2y = 6 --- y = 3
B. 3x + 2y = -6 --- y = -3
C. 3x - 2y = 6 ----- y = -3
D. 2x - 3y = 6 --- y = -2
E. -2x - 3y = 6 --- y =-2
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Intern
Joined: 22 Aug 2014
Posts: 42
Re: Line k is in the rectangular coordinate system. If the x-intercept of [#permalink]

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27 Mar 2015, 03:10
1
KUDOS
Bunuel wrote:
Line k is in the rectangular coordinate system. If the x-intercept of k is -2, and the y-intercept is 3, which of the following is an equation of line k?

A. -3x + 2y = 6
B. 3x + 2y = -6
C. 3x - 2y = 6
D. 2x - 3y = 6
E. -2x - 3y = 6

Kudos for a correct solution.

Two points given are: (-2, 0) & (0,3)
slope = (Y2-Y1)/(X2-X1)

slope = 3/2

Eqn of line: y= mx+c

y = 3x/2 + c - - ---- (1)

Subs pt (-2,0) in eqn 1

C = 3

y = (3/2)*x + 3

2y = 3x + 6

2y - 3x = 6

Option A
Manager
Joined: 31 Jan 2012
Posts: 86
Re: Line k is in the rectangular coordinate system. If the x-intercept of [#permalink]

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27 Mar 2015, 07:33
3
KUDOS
Bunuel wrote:
Line k is in the rectangular coordinate system. If the x-intercept of k is -2, and the y-intercept is 3, which of the following is an equation of line k?

A. -3x + 2y = 6
B. 3x + 2y = -6
C. 3x - 2y = 6
D. 2x - 3y = 6
E. -2x - 3y = 6

Kudos for a correct solution.

Two points through which the line passes are (-2,0) and (0,3)

slope = 3/2

equation: y = 3/2x+3
-3x+2y = 6

Math Expert
Joined: 02 Sep 2009
Posts: 43896
Line k is in the rectangular coordinate system. If the x-intercept of [#permalink]

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30 Mar 2015, 02:57
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
Bunuel wrote:
Line k is in the rectangular coordinate system. If the x-intercept of k is -2, and the y-intercept is 3, which of the following is an equation of line k?

A. -3x + 2y = 6
B. 3x + 2y = -6
C. 3x - 2y = 6
D. 2x - 3y = 6
E. -2x - 3y = 6

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:
Attachment:

findeq_exp (1).png [ 43.38 KiB | Viewed 2100 times ]

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Re: Line k is in the rectangular coordinate system. If the x-intercept of [#permalink]

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08 Apr 2015, 08:34
I recently went through the GMATClub Quant book and thought the intercept formula would work perfectly here. This formula would save a lot of time.

$$\frac{x}{a}$$+$$\frac{y}{b}$$=1

Where,
a is the x intercept
b is the y intercept

$$\frac{x}{-2}$$+$$\frac{y}{3}$$=1

-3x+2y=6

Director
Joined: 07 Aug 2011
Posts: 578
GMAT 1: 630 Q49 V27
Re: Line k is in the rectangular coordinate system. If the x-intercept of [#permalink]

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08 Apr 2015, 09:01
Bunuel wrote:
Line k is in the rectangular coordinate system. If the x-intercept of k is -2, and the y-intercept is 3, which of the following is an equation of line k?

A. -3x + 2y = 6
B. 3x + 2y = -6
C. 3x - 2y = 6
D. 2x - 3y = 6
E. -2x - 3y = 6

Kudos for a correct solution.

as X-intercept is -ive and Y intercept is positive , the slope of line is +ive (3/2) and line will go through I, II, III quadrants.

Y= 3/2X + C

C is nothing else but y intercept = 3 .

Y= 3/2X + 3
2Y = 3X + 6

option A
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Director
Joined: 04 Jun 2016
Posts: 642
GMAT 1: 750 Q49 V43
Re: Line k is in the rectangular coordinate system. If the x-intercept of [#permalink]

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14 Jul 2016, 08:56
Bunuel wrote:
Line k is in the rectangular coordinate system. If the x-intercept of k is -2, and the y-intercept is 3, which of the following is an equation of line k?

A. -3x + 2y = 6
B. 3x + 2y = -6
C. 3x - 2y = 6
D. 2x - 3y = 6
E. -2x - 3y = 6

Kudos for a correct solution.

It will if you remember
Y intercept = b = 3(given in question)
x intercept = -b/m = -2(Given in question)

So
-2=-3/m
m=3/2

Slope = 3/2
Equation of line is y-mx+b
y=3/2 x + 3
multiply both side by 2
2y=3x+6
take 3x to the L.H.S.
-3x+2x=6

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Posts: 13762
Re: Line k is in the rectangular coordinate system. If the x-intercept of [#permalink]

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20 Jan 2018, 18:05
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Line k is in the rectangular coordinate system. If the x-intercept of   [#permalink] 20 Jan 2018, 18:05
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