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thanks , i also got the following explanation and dont understand the logic behind their deduction from 1 ,

Explanation

If a line has negative slope, the intercepts will have the same sign. So if we can find the sign of the x-intercept, we can answer the question.

Statement (1) is insufficient. It's possible that both intercepts are negative, for instance if the x-intercept is -4, the y-intercept could be -2. This is a relatively flat slope--as it turns out, it's true if the slope is greater than -1. It's also possible that both intercepts are positive. For instance, if the x-intercept is 3, the y-intercept could be 5. The negative slope here is steeper--in general, less than -1.

Statement (2) is also insufficient. Such a slope is relatively steep, but it could result in positive or negative intercepts--the slope of the line doesn't determine the location of the line.

Taken together, the statements are sufficient. In (1), we learned that if the slope is less than -1, both intercepts are positive. Since the slope is less than -2, both intercepts must be positive. Choice (C) is correct.

thanks , i also got the following explanation and dont understand the logic behind their deduction from 1 ,

Explanation

If a line has negative slope, the intercepts will have the same sign. So if we can find the sign of the x-intercept, we can answer the question.

Statement (1) is insufficient. It's possible that both intercepts are negative, for instance if the x-intercept is -4, the y-intercept could be -2. This is a relatively flat slope--as it turns out, it's true if the slope is greater than -1. It's also possible that both intercepts are positive. For instance, if the x-intercept is 3, the y-intercept could be 5. The negative slope here is steeper--in general, less than -1.

Statement (2) is also insufficient. Such a slope is relatively steep, but it could result in positive or negative intercepts--the slope of the line doesn't determine the location of the line.

Taken together, the statements are sufficient. In (1), we learned that if the slope is less than -1, both intercepts are positive. Since the slope is less than -2, both intercepts must be positive. Choice (C) is correct.

Can you help ?

thanks

proceed graphically and check the slope, 1) when the intercepts are in first quadrant, you will see the slope should be less than tan(135) i.e. less than -1 to satisfy the condition y>x intercept. (at -1 you will see x=y intercept) similarly, when in third quadrant slope should be greater than tan (135) i.e. -1

insufficient

2) insufficient

both 1 and 2 slope less than -2 i.e. less than -1 hence both intercept are positive.

hope this clarifies
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In the xy-plane, if line k has negative slope, is the y-intercept of line k positive?

Equation of a line in point intercept form is \(y=mx+b\), where: \(m\) is the slope of the line and \(b\) is the y-intercept of the line (the value of \(y\) for \(x=0\)). So, basically we are asked whether \(b>0\).

(1) The x-intercept of line k is less than the y-intercept of line k --> x-intercept is value of \(x\) for \(y=0\), so it's \(-\frac{b}{m}\). The statement says that: \(-\frac{b}{m}<b\) --> multiply by negative \(m\) and flip the sign of the inequality: \(-b>bm\) --> \(b(m+1)<0\). Now, in order \(b>0\) to be true \(m+1\) should be negative, so the question becomes: is \(m+1<0\)? --> is \(m<-1\). We don't know that. Not sufficient.

(2) The slope of line k is less than -2. Insufficient on its own.

(1)+(2) From (1) the question became: "is \(m<-1\)?" and (2) says that \(m<-2\). Sufficient.

I have the same doubt as vipulgoel, however i couldn't understand your follow-up explanation. Since we know m is negative, shouldnt we take the sign into consideration ? Could you please explain what do you mean by "you do not substitute a variable say, x by -x" ?

I have the same doubt as vipulgoel, however i couldn't understand your follow-up explanation. Since we know m is negative, shouldnt we take the sign into consideration ? Could you please explain what do you mean by "you do not substitute a variable say, x by -x" ?

Thanks.

Say it's given that x=a, and you know that x is negative do you substitute x by -x in this case? No.
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Re: In the xy-plane, if line k has negative slope, is the [#permalink]

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06 Nov 2015, 21:08

hi, Let me try , y = mx+ c is a general form, irrespective of slope, first just write x intercept (without considering - ve slope), now as Bunuel did multiply with -m(negative slope on both sides, that's how -ve slope comes in picture)

Re: In the xy-plane, if line k has negative slope, is the [#permalink]

Show Tags

06 Sep 2017, 19:47

Bluelagoon wrote:

In the xy-plane, if line k has negative slope, is the y-intercept of line k positive?

(1) The x-intercept of line k is less than the y-intercept of line k.

(2) The slope of line k is less than -2.

It is a DS question, can you help and explain the answer?

Before we start let's revise a rule, which says that if a line has -ve slope, then either both the intercept will be -ve or both will be +ve. They cannot have different sign.

or

the line can pass from (0,0) i.e origin we are not considering this case.

Answer: C

Let's say X intercept is A and Y intercept is B

1)

says A < B ...(I) now as the slope is -ve. A and B both can be -ve or +ve. Insufficient.

2)

slope is -2. Formula of slope is \frac{Y-intercept}{X-Intercept} so, \frac{B}{A} = -2 ...(II) again, A and B both can be -ve or +ve. Insufficient

Together

from II, \frac{B}{-2} = A substitute the above value in I, \frac{B}{-2} < B Multiply the above fraction by -2, B > -2B 3B > 0, hence B is greater than 0. sufficient

Re: In the xy-plane, if line k has negative slope, is the [#permalink]

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06 Sep 2017, 19:48

Bluelagoon wrote:

In the xy-plane, if line k has negative slope, is the y-intercept of line k positive?

(1) The x-intercept of line k is less than the y-intercept of line k.

(2) The slope of line k is less than -2.

It is a DS question, can you help and explain the answer?

Before we start let's revise a rule, which says that if a line has -ve slope, then either both the intercept will be -ve or both will be +ve. They cannot have different sign.

or

the line can pass from (0,0) i.e origin we are not considering this case.

Answer: C

Let's say X intercept is A and Y intercept is B

1)

says A < B ...(I) now as the slope is -ve. A and B both can be -ve or +ve. Insufficient.

2)

slope is -2. Formula of slope is \frac{Y-intercept}{X-Intercept} so, \frac{B}{A} = -2 ...(II) again, A and B both can be -ve or +ve. Insufficient

Together

from II, \frac{B}{-2} = A substitute the above value in I, \frac{B}{-2} < B Multiply the above fraction by -2, B > -2B 3B > 0, hence B is greater than 0. sufficient

The slope of a line passing through (1, 0) and (0, 1.5) is -1.5, which is not less than -2, as per (2). The slope of a line passing through (-1.5, 0) and (0, -1) is -0.67, which is not less than -2, as per (2).
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The slope of a line passing through (1, 0) and (0, 1.5) is -1.5, which is not less than -2, as per (2). The slope of a line passing through (-1.5, 0) and (0, -1) is -0.67, which is not less than -2, as per (2).

Thanks Bunuel , i realized my mistake slope of Line 1 (-1/1.5) is not less than (-2), Line 1 is not possible.

I must have been half asleep while solving this problem

Re: In the xy-plane, if line k has negative slope, is the [#permalink]

Show Tags

06 Nov 2017, 01:25

Bunuel wrote:

In the xy-plane, if line k has negative slope, is the y-intercept of line k positive?

Equation of a line in point intercept form is \(y=mx+b\), where: \(m\) is the slope of the line and \(b\) is the y-intercept of the line (the value of \(y\) for \(x=0\)). So, basically we are asked whether \(b>0\).

(1) The x-intercept of line k is less than the y-intercept of line k --> x-intercept is value of \(x\) for \(y=0\), so it's \(-\frac{b}{m}\). The statement says that: \(-\frac{b}{m}<b\) --> multiply by negative \(m\) and flip the sign of the inequality: \(-b>bm\) --> \(b(m+1)<0\). Now, in order \(b>0\) to be true \(m+1\) should be negative, so the question becomes: is \(m+1<0\)? --> is \(m<-1\). We don't know that. Not sufficient.

(2) The slope of line k is less than -2. Insufficient on its own.

(1)+(2) From (1) the question became: "is \(m<-1\)?" and (2) says that \(m<-2\). Sufficient.

Answer: C.

Hi Bunuel,

I have doubt here.. can you please help me to understand it if -b/m<b, then can we write m>-1?? by cancelling b on both sides.

In the xy-plane, if line k has negative slope, is the y-intercept of line k positive?

Equation of a line in point intercept form is \(y=mx+b\), where: \(m\) is the slope of the line and \(b\) is the y-intercept of the line (the value of \(y\) for \(x=0\)). So, basically we are asked whether \(b>0\).

(1) The x-intercept of line k is less than the y-intercept of line k --> x-intercept is value of \(x\) for \(y=0\), so it's \(-\frac{b}{m}\). The statement says that: \(-\frac{b}{m}<b\) --> multiply by negative \(m\) and flip the sign of the inequality: \(-b>bm\) --> \(b(m+1)<0\). Now, in order \(b>0\) to be true \(m+1\) should be negative, so the question becomes: is \(m+1<0\)? --> is \(m<-1\). We don't know that. Not sufficient.

(2) The slope of line k is less than -2. Insufficient on its own.

(1)+(2) From (1) the question became: "is \(m<-1\)?" and (2) says that \(m<-2\). Sufficient.

Answer: C.

Hi Bunuel,

I have doubt here.. can you please help me to understand it if -b/m<b, then can we write m>-1?? by cancelling b on both sides.

No. You cannot reduce an inequality by a variable unless you know its sign. If the variable is positive you should keep the sign but if the variable is negative you should flip the sign of the inequality.
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