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In the x-y plane, there is line K, (x/a)+(y/b)=1. What is the y-inter

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In the x-y plane, there is line K, (x/a)+(y/b)=1. What is the y-inter  [#permalink]

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New post 24 Jan 2017, 02:49
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In the x-y plane, there is line K, (x/a)+(y/b)=1. What is the y-intercept of line K?

1) a=b
2) b=5

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Re: In the x-y plane, there is line K, (x/a)+(y/b)=1. What is the y-inter  [#permalink]

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New post 24 Jan 2017, 06:11
Y=b-(bx/a)
Y intercept is when x=0

(1) y=b
No value of b
Insuff

(2)b=5
As y=b=5
Y intercept = (0,5)
Sufficient

And B

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Re: In the x-y plane, there is line K, (x/a)+(y/b)=1. What is the y-inter  [#permalink]

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New post 24 Jan 2017, 09:45
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MathRevolution wrote:
In the x-y plane, there is line K, (x/a) + (y/b) = 1. What is the y-intercept of line K?

1) a = b
2) b = 5


I like this question a lot!

Target question: What is the y-intercept of line K?
Given: The equation of line K is (x/a) + (y/b) = 1

This is a great candidate for rephrasing the target question.
If we can rewrite the equation in slope y-intercept form, then this will help us identify the y-intercept of the line.

Slope y-intercept form looks like this y = mx + q, where m is the slope of the line, and q is the y-intercept.
So, let's take the equation for line L and rewrite it in slope y-intercept form

Given: (x/a) + (y/b) = 1
Eliminate the fractions by multiplying both sides by ab to get: bx + ay = ab
Subtract bx from both sides; ay = -bx + ab
Divide both sides by a to get: y = (-b/a)x + b
So, the slope of like K will by -b/a, and the y-intercept of line K will be b.
Since we're trying to determine the y-intercept, we can rephrase the target question...
REPHRASED target question: What is the value of b?

Now onto the statements....

Statement 1: a = b
This is not enough information to determine the EXACT value of b.
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: b = 5
PERFECT! This is exactly the information we are looking for! (we now know that 5 is the y-intercept of like K)
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Answer: B

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Re: In the x-y plane, there is line K, (x/a)+(y/b)=1. What is the y-inter  [#permalink]

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New post 26 Jan 2017, 00:55
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==> If you modify the original condition and the question, the y-intercept is the value of y when x=0, so if you substitute x=0, from y/b=1, you get y=b, so you only need to know b. According to con 2), it is unique and sufficient.

Therefore, the answer is B.
Answer: B
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Re: In the x-y plane, there is line K, (x/a)+(y/b)=1. What is the y-inter  [#permalink]

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New post 25 Jun 2018, 10:51
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Re: In the x-y plane, there is line K, (x/a)+(y/b)=1. What is the y-inter &nbs [#permalink] 25 Jun 2018, 10:51
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