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30 Jul 2018, 08:28
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C
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Difficulty:
85%
(hard)
Question Stats:
60% (02:51) correct
40%
(03:05)
wrong
based on 210
sessions
History
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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
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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01 Aug 2018, 17:01
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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
General Discussion
30 Jul 2018, 09:04
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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
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