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

Question

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

BrentGMATPrepNow · Accepted Answer

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

Answer: C

Cheers,
Brent

souvonik2k · Answer

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).

chetan2u · Answer

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

bumpbot · Answer

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

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