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# In the xy-coordinate system, if (a,b) and (a+3, b+k) are two

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In the xy-coordinate system, if (a,b) and (a+3, b+k) are two [#permalink]  29 Jul 2020, 10:47
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77% (01:22) correct 22% (01:41) wrong based on 9 sessions
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
[Reveal] Spoiler: OA

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Re: In the xy-coordinate system, if (a,b) and (a+3, b+k) are two [#permalink]  29 Jul 2020, 11:07
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Expert's post
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

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

Cheers,
Brent
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Joined: 02 May 2020
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Kudos [?]: 67 [0], given: 14

Re: In the xy-coordinate system, if (a,b) and (a+3, b+k) are two [#permalink]  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

Re: In the xy-coordinate system, if (a,b) and (a+3, b+k) are two   [#permalink] 29 Jul 2020, 11:33
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