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If the x-intercept of a line l is a and y intercept is b. Is the slope

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rheam25
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If the x-intercept of a line l is a and y intercept is b. Is the slope [#permalink] New post   01 Jun 2020, 05:42
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If the x-intercept of a line l is a and y intercept is b. Is the slope of line l > \(\frac{ 1}{3 }\)?

1. a < b
2. a, b > 0
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nick1816
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Re: If the x-intercept of a line l is a and y intercept is b. Is the slope [#permalink] New post   01 Jun 2020, 17:18
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Statement 1 -
Attachment:
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Untitled.png [ 8.15 KiB | Viewed 4962 times ]


Statement 2-

The angle between the line, whose x and y intercepts both are positive, and +ve direction of the x-axis is between 90 and 180. Hence slope of the line is always negative (can't be greater than 1/3).

Sufficient
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Re: If the x-intercept of a line l is a and y intercept is b. Is the slope [#permalink] New post   03 Jun 2020, 08:06
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rheam25 wrote:
If the x-intercept of a line l is a and y intercept is b. Is the slope of line l > \(\frac{ 1}{3 }\)?

1. a < b
2. a, b > 0


I'd do this as Nick did above -- by drawing pictures to see what results you can get. Using Statement 1, you could have a negative x-intercept and a positive y-intercept. Then, if the x-intercept is close to the origin, the slope of the line can be very large. But if both intercepts are positive, which is also possible, the slope will be negative. So we can't be sure if it's greater than 1/3. If Statement 2 means "a > 0 and b > 0", then it ensures the slope is negative, so ensures the answer to the question is "no", and is sufficient, and the answer is B.

But I hope in the source that Statement 2 isn't written the way it's written above. You can't write inequalities that way (as written, it appears we have a sequence or set on one side of the inequality, which makes no sense), and you'll never see notation like that on the GMAT (or in any other decent math book).
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Re: If the x-intercept of a line l is a and y intercept is b. Is the slope [#permalink] New post   03 Jun 2020, 10:17
IanStewart wrote:
rheam25 wrote:
If the x-intercept of a line l is a and y intercept is b. Is the slope of line l > \(\frac{ 1}{3 }\)?

1. a < b
2. a, b > 0


I'd do this as Nick did above -- by drawing pictures to see what results you can get. Using Statement 1, you could have a negative x-intercept and a positive y-intercept. Then, if the x-intercept is close to the origin, the slope of the line can be very large. But if both intercepts are positive, which is also possible, the slope will be negative. So we can't be sure if it's greater than 1/3. If Statement 2 means "a > 0 and b > 0", then it ensures the slope is negative, so ensures the answer to the question is "no", and is sufficient, and the answer is B.

But I hope in the source that Statement 2 isn't written the way it's written above. You can't write inequalities that way (as written, it appears we have a sequence or set on one side of the inequality, which makes no sense), and you'll never see notation like that on the GMAT (or in any other decent math book).


Can we write the equation of slope as 3y = x+b
And since we want slope greater than 1/3 which is 0.333
1/4 < 1/3
Equation of line with bigger slope is 4y=x+b
Are we plotting points on the equation 4y=x+b?
Why did you took slope negative when both value of X and Y are positive. Kindly explain.

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Re: If the x-intercept of a line l is a and y intercept is b. Is the slope [#permalink] New post   04 Jun 2020, 05:22
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yashikaaggarwal wrote:
Can we write the equation of slope as 3y = x+b
And since we want slope greater than 1/3 which is 0.333
1/4 < 1/3
Equation of line with bigger slope is 4y=x+b
Are we plotting points on the equation 4y=x+b?
Why did you took slope negative when both value of X and Y are positive. Kindly explain.


I'm not following where you get "1/4" from. As I said in my post, I would answer this question visually, and not algebraically - trying to use algebra for questions like this is either going to be difficult or impossible.


yashikaaggarwal wrote:
Why did you took slope negative when both value of X and Y are positive. Kindly explain.


It's not x and y that are both positive. It's the x-intercept and y-intercept of the line that are both positive. If the y-intercept is positive, the line meets the y-axis above the origin (0,0). If the x-intercept is positive, the line meets the x-axis to the right of the origin. So the line needs to fall as it moves from the y-axis to the right, if it hits the x-axis to the right of (0, 0), and that means the slope is negative. That's easier to see just by drawing pictures of lines with positive x- and y-intercepts.
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Re: If the x-intercept of a line l is a and y intercept is b. Is the slope [#permalink] New post   13 Jun 2020, 23:51
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x/a + y/b =1 >> ay = ab - bx >> y= -(b/a)x + b
slope is -b/a
question becomes - Is -b/a > 1/3
-3b>a
is a+ 3b <0

(1) a<b
if both a and b are negative then the answer is yes
if both are positive then answer is no
NS

(2)a,b>0

a+ 3b< 0 will never hold
hence sufficient
Thus , (B)
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Re: If the x-intercept of a line l is a and y intercept is b. Is the slope [#permalink] New post   08 Aug 2021, 11:26
Y intercept / X intercept =b/a
So, slope=(-b/a)

1) a<b
Here if a>0 n b>0 then slope will be negative

NO.

If a<0 & b>0>a
Then slope will be greater than 1.

YES.
So , insufficient.

2)a,b >0
then slope will be negative which means that it will definetely be less than 1/3.

SUFFICIENT.

B it is..

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Re: If the x-intercept of a line l is a and y intercept is b. Is the slope [#permalink] New post   01 Dec 2022, 18:58
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Re: If the x-intercept of a line l is a and y intercept is b. Is the slope [#permalink]
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