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In the xy-coordinate system, if(a, b)

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In the xy-coordinate system, if(a, b) [#permalink] New post 08 Jun 2019, 04:29
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In the xy-coordinate system, if(a, b) and (a – 4, b + k) are two points on the line x = 2y + 8, then what is the value of k?


A. –4
B. –2
C. 1/2
D. 1
E. 4
[Reveal] Spoiler: OA
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Re: In the xy-coordinate system, if(a, b) [#permalink] New post 10 Jun 2019, 09:30
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dvk007 wrote:
In the xy-coordinate system, if (a, b) and (a – 4, b + k) are two points on the line x = 2y + 8, then what is the value of k?


A. –4
B. –2
C. 1/2
D. 1
E. 4


Key Concept: If a point lies on a given line (or curve), then the x- and y-coordinates of that point must satisfy the equation of that line (or curve)

So, we can conclude that:
x = a and y = b is a solution to the equation x = 2y + 8
and
x = a–4 and y = b+k is a solution to the equation x = 2y + 8

Let's deal with each case.
If x = a and y = b is a solution to the equation x = 2y + 8, then we can replace x and y with a and b
We get: a = 2b + 8
Rewrite as: a - 2b = 8


If x = a–4 and y = b+k is a solution to the equation x = 2y + 8, then we can replace x and y with a-4 and b+k
We get: a-4 = 2(b+k) + 8
Expand: a - 4 = 2b + 2k + 8
Add 4 to both sides to get: a = 2b + 2k + 12
Subtract 2b from both sides: a - 2b = 2k + 12

We now have two equations:
a - 2b = 2k + 12
a - 2b = 8

Subtract the bottom equation from the top equation to get: 0 = (2k + 12) - 8
Simplify: 0 = 2k + 4
So: -4 = 2k
Solve: k = -2

Answer: B

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com
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Re: In the xy-coordinate system, if(a, b)   [#permalink] 10 Jun 2019, 09:30
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