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# What is the equation of line b which is parallel to line a?

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Math Expert
Joined: 02 Sep 2009
Posts: 58464
What is the equation of line b which is parallel to line a?  [#permalink]

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30 Aug 2018, 05:15
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Difficulty:

25% (medium)

Question Stats:

73% (01:06) correct 27% (00:55) wrong based on 55 sessions

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What is the equation of line b which is parallel to line a?

(1) The slope of line a is 3/4 and it crosses the y-axis at 3.

(2) Line b has no point in common with line a.

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Re: What is the equation of line b which is parallel to line a?  [#permalink]

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30 Aug 2018, 05:22
Bunuel wrote:
What is the equation of line b which is parallel to line a?

(1) The slope of line a is 3/4 and it crosses the y-axis at 3.

(2) Line b has no point in common with line a.

CONCEPT: For Parallel Lines, Slopes are equal i.e. $$m_1 = m_2$$

Question : Equation of line b = ?

Statement 1: The slope of line a is 3/4 and it crosses the y-axis at 3.

This statement informs us about slope of line a i.e. slope of line b as well (as both slopes are equal)
but Y-intercept of line b is still unknown hence
NOT SUFFICIENT

Statement 2: Line b has no point in common with line a

This statement also refers to the given information that lines are parallel (Two lines will not share any common point ONLY if the two lines are parallel hence USELESS statement for any purpose

NOT SUFFICIENT

Combining the statements

Combining the statements doesn't make sense because second statement is useless as we already knew that lines a and b are parallel and first statement alone fails to give us any information about the Y-intercept of line a hence

NOT SUFFICIENT

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What is the equation of line b which is parallel to line a?  [#permalink]

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30 Aug 2018, 09:26
Bunuel wrote:
What is the equation of line b which is parallel to line a?

(1) The slope of line a is 3/4 and it crosses the y-axis at 3.

(2) Line b has no point in common with line a.

Question stem:- What is the equation of line b which is parallel to line a
a) implies slope of line b-slope of line a =m (say)
b) Equation of line 'b' is in the form y=mx+c, where c(y-intercept of line b) can be 0, +/-. However, we need an unique value of 'c' so that equation of line 'b' be unique.

St1:-The slope of line a is 3/4 and it crosses the y-axis at 3.
Or, m=3/4 . Value of c is not known. c can have any value.
So, equation of line b is not unique.
Insufficient.

St2:- Line b has no point in common with line a.
This is the definition of parallel lines and this information is already stated in question stem. No new info.
Insufficient.

Combined, No new info.
Insufficient.

Ans. (E)
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What is the equation of line b which is parallel to line a?   [#permalink] 30 Aug 2018, 09:26
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