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In the xy-coordinate system, if (a,b) and (a+3, b+k) are two
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29 Jul 2020, 10:47
29 Jul 2020, 10:47
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In the xy-coordinate system, if (a,b) and (a+3, b+k) are two points on the line defined by the equation x=3y-7, then k=?
A. 9
B. 3
C. 7/3
D. 1
E. 1/3
Kudos for the right answer and explanation
A. 9
B. 3
C. 7/3
D. 1
E. 1/3
Kudos for the right answer and explanation
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: In the xy-coordinate system, if (a,b) and (a+3, b+k) are two
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29 Jul 2020, 11:07
29 Jul 2020, 11:07
1
Carcass wrote:
In the xy-coordinate system, if (a,b) and (a+3, b+k) are two points on the line defined by the equation x=3y-7, then k=?
A. 9
B. 3
C. 7/3
D. 1
E. 1/3
Kudos for the right answer and explanation
A. 9
B. 3
C. 7/3
D. 1
E. 1/3
Kudos for the right answer and explanation
Key Concept: If a point lies ON a line, then the coordinates (x and y) of that point must SATISFY the equation of that line.
Given equation: x = 3y - 7
One point ON the line is (a, b)
So, we can write: a = 3b - 7
Another point ON the line is (a + 3, b + k)
So, we can write: a + 3 = 3(b + k) - 7
Expand: a + 3 = 3b + 3k - 7
Subtract 3 from both sides to get: a = 3b + 3k - 10
We now two equations:
a = 3b + 3k - 10
a = 3b - 7
Subtract the bottom equation from the top equation to get: 0 = 3k - 3
Add 3 to both sides: 3 = 3k
Solve: k = 1
Answer: D
Cheers,
Brent
Re: In the xy-coordinate system, if (a,b) and (a+3, b+k) are two
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29 Jul 2020, 11:33
29 Jul 2020, 11:33
Equation of line is x=3y-7
It can be written as
y = (1/3)*x + (7/3)
=> slope = 1/3
Since, (a,b) and (a+3, b+k) also lie on the line
slope can also be written as
slope = (b+k-b)/(a+3-a)
=> 1/3 = k/3
=> k = 1
So, the answer is D.
It can be written as
y = (1/3)*x + (7/3)
=> slope = 1/3
Since, (a,b) and (a+3, b+k) also lie on the line
slope can also be written as
slope = (b+k-b)/(a+3-a)
=> 1/3 = k/3
=> k = 1
So, the answer is D.
