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What is the equation of the line L? 02 Sep 2019, 00:14
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C
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35% (medium)

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65% (01:18) correct 35% (01:24) wrong based on 63 sessions

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What is the equation of the line L?

(1) A line M, perpendicular to line L, is at an angle of 135° with the x-axis.
(2) The y intercept of line L is -2
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C
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What is the equation of the line L? 02 Sep 2019, 01:31
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What is the equation of the line L?

(1) A line M, perpendicular to line L, is at an angle of 135° with the x-axis.
(2) The y intercept of line L is -2
Show more

Sometimes imagining a scenario helps you in simplifying a question..

So, what comes to your mind when you think of a line?
It is joining of points in x-y plane..
(a) We can draw a line if we know any points
(b) We can draw a line if we know slope and any one point on line

(1) A line M, perpendicular to line L, is at an angle of 135° with the x-axis.
Point (b) above. We know the slope - It is at 45 degree with x-axis, but it can be anywhere on the x-y plane.
Insuff

(2) The y intercept of line L is -2.
Point (a). We know one point as (-2,0), so we require the SECOND point or the slope..
Insuff

Combined..
Point (b) .. We know slope and one point, so we can draw the line and find equation
Sufficient
C
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What is the equation of the line L? 02 Sep 2019, 05:00
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Note that line M can make an angle of 135 degrees with the x axis while having both a positive and negative slope. Therefore the slope of line L can have changing signs.

Answer is E.

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What is the equation of the line L? 02 Sep 2019, 05:50
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truplayer257
Note that line M can make an angle of 135 degrees with the x axis while having both a positive and negative slope. Therefore the slope of line L can have changing signs.

Answer is E.

Posted from my mobile device
Show more


Thats not correct...
The angle is always calculated anticlockwise from x axis..
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What is the equation of the line L? 02 Sep 2019, 06:27
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chetan2u
truplayer257
Note that line M can make an angle of 135 degrees with the x axis while having both a positive and negative slope. Therefore the slope of line L can have changing signs.

Answer is E.

Posted from my mobile device


Thats not correct...
The angle is always calculated anticlockwise from x axis..
Show more

Hi Chetan2u,

Yes, I understand that but what I'm trying to say is that line M can have both a negative or a positive slope while making an angle of 135 degrees with the x-axis. Therefore, although in statement 2 we are told that the y-intercept of line L is 2, we still cannot come up with its equation since we don't know if the slope is positive or negative. So I think answer is E.
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What is the equation of the line L? 02 Sep 2019, 06:39
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truplayer257
Note that line M can make an angle of 135 degrees with the x axis while having both a positive and negative slope. Therefore the slope of line L can have changing signs.

Answer is E.

Posted from my mobile device


Thats not correct...
The angle is always calculated anticlockwise from x axis..
Show more
chetan2u
So figure A and b are correct in attached image and A' and B' are wrong.Is my understanding correct?So we can say we start calculating angle from RHS of line till the line.

Also how did we get slope from 1.Is it becuase tan (135) =-1 and since both are perpendiclaur line L will have slope 1
Any way other than tan?

also u said

(1) A line M, perpendicular to line L, is at an angle of 135° with the x-axis.
Point (b) above. We know the slope - It is at 45 degree with x-axis, but it can be anywhere on the x-y plane.
Insuff
how slope is 45 degree if line is at angle of 135 degree with x axis.
isnot slope the tan of angle made by line with x axis
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What is the equation of the line L? 02 Sep 2019, 10:18
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vanam52923
chetan2u
truplayer257
Note that line M can make an angle of 135 degrees with the x axis while having both a positive and negative slope. Therefore the slope of line L can have changing signs.

Answer is E.

Posted from my mobile device


Thats not correct...
The angle is always calculated anticlockwise from x axis..
chetan2u
So figure A and b are correct in attached image and A' and B' are wrong.Is my understanding correct?So we can say we start calculating angle from RHS of line till the line.

Also how did we get slope from 1.Is it becuase tan (135) =-1 and since both are perpendiclaur line L will have slope 1
Any way other than tan?

also u said

(1) A line M, perpendicular to line L, is at an angle of 135° with the x-axis.
Point (b) above. We know the slope - It is at 45 degree with x-axis, but it can be anywhere on the x-y plane.
Insuff
how slope is 45 degree if line is at angle of 135 degree with x axis.
isnot slope the tan of angle made by line with x axis
Show more

truplayer257 and vanam52923
Please check my initial post. I have added a sketch to it. The doubt should get clarified.
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What is the equation of the line L? 02 Sep 2019, 10:58
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Few Things that should be kept in mind before solving this question.

When a line makes an obtuse angle with the positive x-axis, it cannot be used to determine the slope, as in this case, line M makes an angle of 135° with the x-axis; the angle consideresd should be less than or equal to 90°. Rather, we use the complimentary angle that it makes with the x-axis i.e. a 45° angle, indicating that the slope is negative. Refer to the attachment A1 for better understanding.

Second thing to keep in mind is that when a line makes a 45° angle with the positive x-axis, it means that when x increases/decreases by a certain value, y increases/decrease by the same value and vice-versa. This means that the slope is 1, as slope is nothing else but the rate of change of the y and x, which is constant in this case. Further, it cannot be assumed the line in consideration passes through the origin. It may make a 45° angle with the x-axis passing through, for instance, (2,0). Refer to attachment A2 for better understanding.

Coming back to the question.

Statement 1
This says that a line perpendicular to line L makes a 135° angle with the x-axis. From this we can deduce that line L is at a 45° with the x-axis. We know that the slope is 1, like explained earlier. But we don't have other information to deduce the equation of the line from.

Insufficient

Statement 2
This statement says that the y-intercept is -2, however, we don't have sufficient information to deduce the equation of the line from.

Insufficient

Statement 1 & 2 together
We know the slope and the y intercept. From this information, we can deduce x intercept to be 2.
Imagine a line, K, at 45° angle parallel to another line, Z, passing through the origin.
Z will have pass through (0,0) and K might pass through (1,-1), (2,-2), (-1, 1), (-2, 2) etc. Refer attachment A3 for a better understanding.
To conclude, we can say that when a line has slope 1, the x intercept and why intercept have the same numerical value but may differ in signs.

Statements 1 & 2 together are sufficient

Hence, C

Hope this clears everything!
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A3.jpg
A3.jpg [ 114.56 KiB | Viewed 2809 times ]

A2.jpg
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A1.jpg
A1.jpg [ 108.83 KiB | Viewed 2823 times ]

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What is the equation of the line L? 02 Sep 2019, 20:52
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chetan2u
vaibhav1221
What is the equation of the line L?

(1) A line M, perpendicular to line L, is at an angle of 135° with the x-axis.
(2) The y intercept of line L is -2

Sometimes imagining a scenario helps you in simplifying a question..

So, what comes to your mind when you think of a line?
It is joining of points in x-y plane..
(a) We can draw a line if we know any points
(b) We can draw a line if we know slope and any one point on line

(1) A line M, perpendicular to line L, is at an angle of 135° with the x-axis.
Point (b) above. We know the slope - It is at 45 degree with x-axis, but it can be anywhere on the x-y plane.
Insuff

(2) The y intercept of line L is -2.
Point (a). We know one point as (-2,0), so we require the SECOND point or the slope..
Insuff

Combined..
Point (b) .. We know slope and one point, so we can draw the line and find equation
Sufficient
C
Show more
chetan2u
Sorry to trouble you again but this topic always confuses me in graphical approach which is very much time saving .Please reply to following queries.
Thanks

In attached image named X axis cases ,so can i say if it is given that line makes an angle of O(theta in image) with x axis ,so these 4 cases -case 1,2,3,4 in image will bee correct.

In image Y axis cases ,can u tell me which of Case 5 or case 6 will hold ? if it is given line amkes an angle of )(theta) with y axis?
can u tell me which of Case 7 or case 8 will hold ? if it is given line amkes an angle of O(theta) with y axis?

Also very important ,if u see last image named Angle Doubt ,it has diagram with name Case 9
so u said this is not possibel as line makes 135 with x axis so O cannot be 135 because to be greater than 135 it will have to cross perprendicaurl and then it will become like case 1.Is my understanding correct?

Also if line makes obtuse angle with x axis , slope is negative.Is same true for y axis ?

Please answer all these queries.i shall be highly thank ful
Attachments

File comment: Angle doubt
IMG20190903090616.jpg
IMG20190903090616.jpg [ 3.61 MiB | Viewed 2748 times ]

File comment: Y axis cases
IMG20190903090612.jpg
IMG20190903090612.jpg [ 3.89 MiB | Viewed 2743 times ]

File comment: X axis cases
IMG20190903090549.jpg
IMG20190903090549.jpg [ 3.94 MiB | Viewed 2785 times ]

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What is the equation of the line L? 02 Sep 2019, 22:28
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vanam52923
chetan2u
vaibhav1221
What is the equation of the line L?

(1) A line M, perpendicular to line L, is at an angle of 135° with the x-axis.
(2) The y intercept of line L is -2

Sometimes imagining a scenario helps you in simplifying a question..

So, what comes to your mind when you think of a line?
It is joining of points in x-y plane..
(a) We can draw a line if we know any points
(b) We can draw a line if we know slope and any one point on line

(1) A line M, perpendicular to line L, is at an angle of 135° with the x-axis.
Point (b) above. We know the slope - It is at 45 degree with x-axis, but it can be anywhere on the x-y plane.
Insuff

(2) The y intercept of line L is -2.
Point (a). We know one point as (-2,0), so we require the SECOND point or the slope..
Insuff

Combined..
Point (b) .. We know slope and one point, so we can draw the line and find equation
Sufficient
C
chetan2u
Sorry to trouble you again but this topic always confuses me in graphical approach which is very much time saving .Please reply to following queries.
Thanks

In attached image named X axis cases ,so can i say if it is given that line makes an angle of O(theta in image) with x axis ,so these 4 cases -case 1,2,3,4 in image will bee correct.

In image Y axis cases ,can u tell me which of Case 5 or case 6 will hold ? if it is given line amkes an angle of )(theta) with y axis?
can u tell me which of Case 7 or case 8 will hold ? if it is given line amkes an angle of O(theta) with y axis?

Also very important ,if u see last image named Angle Doubt ,it has diagram with name Case 9
so u said this is not possibel as line makes 135 with x axis so O cannot be 135 because to be greater than 135 it will have to cross perprendicaurl and then it will become like case 1.Is my understanding correct?

Also if line makes obtuse angle with x axis , slope is negative.Is same true for y axis ?

Please answer all these queries.i shall be highly thank ful
Show more

Consider only the angles made with the positive x-axis i.e. towards the right of any line segment. In this question Line m makes the an angle of 135° with the positive x-axis, even if positive x-axis is not mentioned. So to clear your doubt, any line that makes an obtuse angle with the positive x-axis has a negative slope.

Your understanding of graphs 1-4 is fine. For graphs 5-8, there is no need to worry about the lines making an angle with the y-axis, as far as I know.
Refer to attachment for graphs 1-4.
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What is the equation of the line L? 02 Sep 2019, 22:48
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thanks a lot man
Also can u clear case 9 ,i know its silly but still
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What is the equation of the line L? 02 Sep 2019, 23:00
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vaibhav1221
thanks a lot man
Also can u clear case 9 ,i know its silly but still
Show more

Yes, θ cannot be 135° because it has to be less than 90° for a simple reason that the line has a positive slope.

Slope measures nothing but the rate of change of y and x. That is why differentiation (dy/dx) gives you the slope because it measures the rate of change.

When a line makes an obtuse angle with the positive x-axis, then the line would lie in the second and fourth quadrant where either x or y is negative, but not both (as is the case when a line is positively sloped, it lies in the first and third quadrant where the sign of rate of change nullifies to become positive), hence the slope is also negative because the change in the value of x or y, depending on whether we are talking about the second or the fourth quadrant will be negative.

Hope this clears your doubt!
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What is the equation of the line L? 02 Sep 2019, 23:10
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vaibhav1221
thanks a lot man
Also can u clear case 9 ,i know its silly but still

Yes, θ cannot be 135° because it has to be less than 90° for a simple reason that the line has a positive slope.

Slope measures nothing but the rate of change of y and x. That is why differentiation (dy/dx) gives you the slope because it measures the rate of change.

When a line makes an obtuse angle with the positive x-axis, then the line would lie in the second and fourth quadrant where either x or y is negative, but not both (as is the case when a line is positively sloped, it lies in the first and third quadrant where the sign of rate of change nullifies to become positive), hence the slope is also negative because the change in the value of x or y, depending on whether we are talking about the second or the fourth quadrant will be negative.

Hope this clears your doubt!
Show more

thank you so much!!!!
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