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In the xy-plane, line a and line b have the same slope. If the y-inter

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In the xy-plane, line a and line b have the same slope. If the y-inter  [#permalink]

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In the xy-plane, line a and line b have the same slope. If the y-intercept of line a is -1, what is the y-intercept of line b ?

(1) The x-intercept of line a is -1.
(2 Line b passes through the point (10, 20).

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Originally posted by monir6000 on 24 Apr 2012, 19:54.
Last edited by Bunuel on 19 Aug 2018, 08:00, edited 3 times in total.
Edited the question
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Re: In the xy-plane, line a and line b have the same slope. If the y-inter  [#permalink]

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New post 24 Apr 2012, 20:39
3
monir6000 wrote:
In the xy plane, line a and b have the same slope. If the y intercept of line a is -1. What is the y-intercept of line b?
(1) the x-intercept of line a is -1
(2) line b passess through the point (10, 20)


given that line a and b are having the same slope... and given the line a y-intercept is -1...we need to find y-intercept of line b

1) x intercept of line a is -1

any line equation is given by y=mx+a for line a
y=mx+b for line b

hence the equation becomes y = mx - 1
for x intercept y becomes 0
0 = mx - 1
mx = 1

so for x intercept to be - 1 then to make that happen x = 1/m = -1
so m should be -1

but this makes the line b equation as y = -x + b

beyond this we cant find... hence not sufficient.. so A and D options are off...

2) line b passes through (10, 20)

y = mx + b

so 20 = 10m + b

two unknowns...we cannot solve

together.. we know that m = - 1 and 20 = 10m + b

so 20 = -10 + b
b = 30 which is the y-intercept of line b

hence C
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Re: In the xy-plane, line a and line b have the same slope. If the y-inter  [#permalink]

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New post 24 Apr 2012, 20:46
2
2
monir6000 wrote:
In the xy plane, line a and b have the same slope. If the y intercept of line a is -1. What is the y-intercept of line b?

(1) the x-intercept of line a is -1
(2) line b passess through the point (10, 20)



In the xy-plane, line a and line b have the same slope. If the y-intercept of line a is -1, what is the y-intercept of line b ?

You don't need any algebra or even drawing, to solve this question. Just try to visualize the info given. First of all notice that "line a and line b have the same slope" means that the lines are parallel.

(1) The x-intercept of line a is -1. We have two points of line a: (0, -1) and (-1, 0), so it's fixed (we can find its equation). But since there are infinitely many parallel lines to line a, then each will have different y-intercept. Not sufficient.

(2 Line b passes through the point (10, 20). We have one point of line a: (0, -1) and one point of line b: (10, 20). We can rotate two parallel lines around these points, which will give different y-intercept of line b. Not sufficient.

(1)+(2) We have fixed line a, and its parallel line b which passes through the point (10, 20), which means that line b is also fixed and we can find its y-intercept (through some particular point, you can draw only one line which will be parallel to some fixed line). Sufficient.

Answer: C.
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Re: In the xy-plane, line a and line b have the same slope. If the y-inter  [#permalink]

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New post 25 Apr 2012, 07:16
Thanks for the quick explanation Bunuel. It takes less time using your method.
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Re: In the xy-plane, line a and line b have the same slope. If the y-inter  [#permalink]

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New post 16 Aug 2018, 08:00
1
monir6000 wrote:
In the xy-plane, line a and line b have the same slope. If the y-intercept of line a is -1, what is the y-intercept of line b ?

(1) The x-intercept of line a is -1. We have two points of line a: (0, -1) and (-1, 0), so it's fixed (we can find its equation). But since there are infinitely many parallel lines to line a, then each will have different y-intercept. Not sufficient.

(2 Line b passes through the point (10, 20).


Dear Moderator,

Came across this question in coordinate geometry, seems like some extra information has inadvertently crept into statement 1. Hope you will look into this . Thank you.
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Re: In the xy-plane, line a and line b have the same slope. If the y-inter  [#permalink]

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New post 16 Aug 2018, 08:04
1
stne wrote:
monir6000 wrote:
In the xy-plane, line a and line b have the same slope. If the y-intercept of line a is -1, what is the y-intercept of line b ?

(1) The x-intercept of line a is -1. We have two points of line a: (0, -1) and (-1, 0), so it's fixed (we can find its equation). But since there are infinitely many parallel lines to line a, then each will have different y-intercept. Not sufficient.

(2 Line b passes through the point (10, 20).


Dear Moderator,

Came across this question in coordinate geometry, seems like some extra information has inadvertently crept into statement 1. Hope you will look into this . Thank you.

_______________
Edited. Thank you.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: In the xy-plane, line a and line b have the same slope. If the y-inter &nbs [#permalink] 16 Aug 2018, 08:04
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