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Thanks for the quick explanation Bunuel. It takes less time using your method.
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monir6000
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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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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(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.

Hi Bunuel,

Iam not sure about what you mean with your explaination with regards to statement 2. What do you mean with rotating two parallel lines around these points, which wil give different y-intercept of line b ?

Thanks in advance!
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Quote:
(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.

Hi Bunuel,

Iam not sure about what you mean with your explaination with regards to statement 2. What do you mean with rotating two parallel lines around these points, which wil give different y-intercept of line b ?

Thanks in advance!

Check below:





Blue one is line a and red one is line b.

You can see that you can get diagram 2 just by rotating blue and red lines around blue and red points in diagram 1.

Attachment:
1.png
1.png [ 13.29 KiB | Viewed 10512 times ]
Attachment:
2.png
2.png [ 6.21 KiB | Viewed 10511 times ]
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Hi Bunuel,

It is now very clear to me what you have stated with regards to rotating the lines.

Thanks a lot!
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Bunuel
monir6000
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.

With the Statement 1, we have both the x and y intercepts of line a. So why do we have different pairs of lines . With the intercepts of both x and y , can't we determine the unique line or unique equation of line a ? Here x intercept is -1 and y-intercept is also -1. Please tell me where i am faltering.

Bunuel
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Bunuel
monir6000
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.

With the Statement 1, we have both the x and y intercepts of line a. So why do we have different pairs of lines . With the intercepts of both x and y , can't we determine the unique line or unique equation of line a ? Here x intercept is -1 and y-intercept is also -1. Please tell me where i am faltering.

Bunuel
jeff

You can determine a unique line for a, but the question is not asking about a -- the question is asking for the y-intercept of b. With statement 1 the only thing we can conclude is that b has the same slope. We still can't determine the y - intercept. For example, the y-intercept of b can be -1 (like a) or it can be -5.
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