GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
In the xy-coordinate system, if(a, b)
[#permalink]
08 Jun 2019, 04:29
08 Jun 2019, 04:29
1
2
Bookmarks
00:00
Question Stats:
78% (01:26) correct
21% (01:46) wrong based on 51 sessions
Hide Show timer Statistics
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
A. –4
B. –2
C. 1/2
D. 1
E. 4
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: In the xy-coordinate system, if(a, b)
[#permalink]
10 Jun 2019, 09:30
10 Jun 2019, 09:30
1
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
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
Re: In the xy-coordinate system, if(a, b)
[#permalink]
10 May 2020, 12:18
10 May 2020, 12:18
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
A. –4
B. –2
C. 1/2
D. 1
E. 4
One fast approach is to recognize that the slope, M, can be calculated if you have two points, using the rise/run formula.
First, rearrange the x=2y+8 to --> y= 1/2x -4. From this we can see the slope is 1/2.
Accordingly, use the provided points to calculate rise/run (Y2-Y1/X2-X1). This can help to get rid of the variables 'a' and 'b' and to therein isolate 'k'.
(b+k - b)/ (a-4 - a) = k / -4
Now, using the previously determined slope of 1/2...
k/-4 = 1/2
k=-2
