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

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Bunuel
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Line k is in the rectangular coordinate system. If the x-intercept of [#permalink] New post   26 Mar 2015, 04:31
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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

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A
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AmoyV
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Re: Line k is in the rectangular coordinate system. If the x-intercept of [#permalink] New post   26 Mar 2015, 07:20
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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

Answer : A
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Re: Line k is in the rectangular coordinate system. If the x-intercept of [#permalink] New post   26 Mar 2015, 07:32
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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
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Re: Line k is in the rectangular coordinate system. If the x-intercept of [#permalink] New post   27 Mar 2015, 02:13
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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

A is the correct answer
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Re: Line k is in the rectangular coordinate system. If the x-intercept of [#permalink] New post   27 Mar 2015, 03:50
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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
Eliminate answer B,C,D and E.
So the answer is A.
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Re: Line k is in the rectangular coordinate system. If the x-intercept of [#permalink] New post   27 Mar 2015, 04:10
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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.



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
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Re: Line k is in the rectangular coordinate system. If the x-intercept of [#permalink] New post   27 Mar 2015, 08:33
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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.


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

slope = 3/2

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

Answer A
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Line k is in the rectangular coordinate system. If the x-intercept of [#permalink] New post   30 Mar 2015, 03:57
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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.


MAGOOSH OFFICIAL SOLUTION:
Attachment:
findeq_exp (1).png
findeq_exp (1).png [ 43.38 KiB | Viewed 11768 times ]
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Re: Line k is in the rectangular coordinate system. If the x-intercept of [#permalink] New post   08 Apr 2015, 09:34
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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

Answer: A
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Re: Line k is in the rectangular coordinate system. If the x-intercept of [#permalink] New post   08 Apr 2015, 10:01
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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Re: Line k is in the rectangular coordinate system. If the x-intercept of [#permalink] New post   14 Jul 2016, 09:56
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

Answer is A
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Re: Line k is in the rectangular coordinate system. If the x-intercept of [#permalink] New post   12 Mar 2018, 06:16
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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.



Equation of LIne

(x/x-intercept)+(y/y-intercept) =1

So

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

After solving

=-3x+2y=6

Hence A is the answer .
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Re: Line k is in the rectangular coordinate system. If the x-intercept of [#permalink] New post   20 Apr 2023, 02:31
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Re: Line k is in the rectangular coordinate system. If the x-intercept of [#permalink]
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