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# In the x-y coordinate plane, lines J, K

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Joined: 12 Sep 2015
Posts: 3907
In the x-y coordinate plane, lines J, K  [#permalink]

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30 Jul 2018, 08:28
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Difficulty:

85% (hard)

Question Stats:

50% (02:36) correct 50% (03:02) wrong based on 68 sessions

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Line J: 4x - 7 = 6y
Line K: 6y + 3x = -2
Line L: 2x = 5 - y

In the x-y coordinate plane, lines J, K and L are defined by the above equations.
Point B is the point of intersection of lines J and K. Point C is the point of intersection of lines K and L.
What is the slope of line segment BC?

A) -3/2
B) -2/3
C) -1/2
D) 1/2
E) 2/3

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Re: In the x-y coordinate plane, lines J, K  [#permalink]

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30 Jul 2018, 09:04
1
GMATPrepNow wrote:
Line J: 4x - 7 = 6y
Line K: 6y + 3x = -2
Line L: 2x = 5 - y

In the x-y coordinate plane, lines J, K and L are defined by the above equations.
Point B is the point of intersection of lines J and K. Point C is the point of intersection of lines K and L.
What is the slope of line segment BC?

A) -3/2
B) -2/3
C) -1/2
D) 1/2
E) 2/3

Draw the lines approximately in the x-y coordinate with the help of the slopes. Refer to the figure in attachment below.
J : y=$$\frac{2}{3}$$x-$$\frac{7}{6}$$
K : y=$$\frac{-x}{2}$$-$$\frac{1}{3}$$
L : y=-2x+5
Point B is the point of intersection of lines J and K. Point C is the point of intersection of lines K and L.
Hence BC lies on line K, which has a slope of $$\frac{-1}{2}$$.
Answer $$\frac{-1}{2}$$ (C).
Attachments

Untitled.jpg [ 12.67 KiB | Viewed 1105 times ]

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In the x-y coordinate plane, lines J, K  [#permalink]

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30 Jul 2018, 09:25
1
GMATPrepNow wrote:
Line J: 4x - 7 = 6y
Line K: 6y + 3x = -2
Line L: 2x = 5 - y

In the x-y coordinate plane, lines J, K and L are defined by the above equations.
Point B is the point of intersection of lines J and K. Point C is the point of intersection of lines K and L.
What is the slope of line segment BC?

A) -3/2
B) -2/3
C) -1/2
D) 1/2
E) 2/3

Great question...
Answer is right there staring at you if you understand it

A point, B ,is at intersection of line J and K and another point, C, is at intersection of K and L.. so points B and C are on line K
When you join B and C, it is nothing but a part of line K..
So slope will be same as that of line K..
$$6y+3x=-2........6y=-3x-2......y=-\frac{3x}{6} -\frac{2}{6}$$
Slope is $$-\frac{3}{6}=\frac{-1}{2}$$

C

Also if you do not get this, other way is..
Take lines J and K
Line J: 4x - 7 = 6y
Line K: 6y + 3x = -2
Two equation two variables, so you will get value of X and y of B
Similarly of C from line K and L..
Slope will be $$\frac{y_B-y_C}{x_B-x_C}$$
You will get answer as -1/2

C
Attachments

PicsArt_07-30-10.08.00.jpg [ 42.81 KiB | Viewed 1078 times ]

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Re: In the x-y coordinate plane, lines J, K  [#permalink]

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01 Aug 2018, 17:01
1
Top Contributor
GMATPrepNow wrote:
Line J: 4x - 7 = 6y
Line K: 6y + 3x = -2
Line L: 2x = 5 - y

In the x-y coordinate plane, lines J, K and L are defined by the above equations.
Point B is the point of intersection of lines J and K. Point C is the point of intersection of lines K and L.
What is the slope of line segment BC?

A) -3/2
B) -2/3
C) -1/2
D) 1/2
E) 2/3

Key Concepts: point B lies on line K, and point C lies on line K
Since both points lie on line K, the slope between points B and C will be the same as the slope of line K.

To find the slope of line K, let's take the equation of line K (6y + 3x = -2), and rewrite it in slope y-intercept form (y = mx + b)
Take: 6y + 3x = -2
Subtract 3x from both sides to get: 6y = -3x - 2
Divide both sides by 6 to get: y = (-3/6)x - 2/6
Simplify to get: y = (-1/2)x - 1/3

So, line K has a slope of -1/2 and a y-intercept of -1/3

Cheers,
Brent
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Re: In the x-y coordinate plane, lines J, K  [#permalink]

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09 Aug 2019, 10:48
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Re: In the x-y coordinate plane, lines J, K   [#permalink] 09 Aug 2019, 10:48
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