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

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In the xy-plane, line a and line b have the same slope. [#permalink] New post 24 Apr 2012, 19:54
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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. 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).
[Reveal] Spoiler: OA

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Last edited by Bunuel on 24 Apr 2012, 20:42, edited 1 time in total.
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Re: In the xy plane, line a and b have the same slope. [#permalink] New post 24 Apr 2012, 20:39
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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 b have the same slope. [#permalink] New post 24 Apr 2012, 20:46
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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. [#permalink] New post 25 Apr 2012, 07:16
Thanks for the quick explanation Bunuel. It takes less time using your method.
Re: In the xy-plane, line a and line b have the same slope.   [#permalink] 25 Apr 2012, 07:16
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