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10 Dec 2019, 02:11
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
68% (01:36) correct
32%
(01:56)
wrong
based on 99
sessions
History
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Time
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Not Attempted Yet
In the xy-plane, line \(\ell\) is parallel to the line \(y = 3x + 2\). If line \(\ell\) passes through the point (1, —1), then line \(\ell\) passes through which of the following points?
I. (2, 2)
II. (0, -2)
III. (-2, -10)
A. I only
B. II only
C. III only
D. I and III only
E. I, II, and III
I. (2, 2)
II. (0, -2)
III. (-2, -10)
A. I only
B. II only
C. III only
D. I and III only
E. I, II, and III
Ansh777
Joined: 03 Nov 2019
Last visit: 06 Jun 2023
Posts: 53
Given Kudos: 128
Location: India
Schools: Booth '24 Columbia CBS '24 Darden '24 Fuqua '24 Haas '24 Harvard '24 LBS '24 Stanford '24 Kellogg '24 Wharton '24
GMAT 1: 710 Q50 V36
Schools: Booth '24 Columbia CBS '24 Darden '24 Fuqua '24 Haas '24 Harvard '24 LBS '24 Stanford '24 Kellogg '24 Wharton '24
GMAT 1: 710 Q50 V36
Posts: 53
10 Dec 2019, 03:46
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L is parallel to y=3x+2 and passes through (1, —1)
since both the lines are parallel therefore there slopes are equal = 3
equation of line L:
(y-y1)/x-x1) = slope
y+1=3*(x-1)
y=3x-4
Now substituting these points in the above equation
I. (2, 2) => (3x-4)=2=y
II. (0, -2) => (3x-4)=-4 is not equal to y (-2)
III. (-2, -10)=> (3x-4)=-10=y
Answer: D
since both the lines are parallel therefore there slopes are equal = 3
equation of line L:
(y-y1)/x-x1) = slope
y+1=3*(x-1)
y=3x-4
Now substituting these points in the above equation
I. (2, 2) => (3x-4)=2=y
II. (0, -2) => (3x-4)=-4 is not equal to y (-2)
III. (-2, -10)=> (3x-4)=-10=y
Answer: D
11 Dec 2019, 00:23
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In this question on Co-ordinate geometry, the concepts being tested are the following:
1)If two lines are parallel, their slopes are equal.
2) When the equation of a line is represented in the Slope-Intercept form i.e. the y=mx+c form, the co-efficient of x represents the slope of the line and c represents the y-intercept of the line.
3) When a line passes through a point, the co-ordinates of that point satisfy the equation of the line when substituted.
With this in mind, let us proceed to analyse the question data. The question says that the line l is parallel to the line represented by y=3x + 2. The slope of this line is 3 and the y-intercept is 2. Therefore, the slope of line l should also be 3, but with a different y-intercept.
So, the equation of line l can be written as y = 3x + k, where k is the y-intercept of line l. Since the line passes through (1,-1), the co-ordinates can be substituted in the equation of line l. Doing this,
-1 = 3*1 + k, which yields k= -4 on solving the equation.
Therefore, equation of line l is y=3x – 4. Now that we know the equation of line l, the only thing left out is for us to substitute the co-ordinates of the points given in the statements and see which ones satisfy the equation.
Substituting (2,2) from statement I, we see that 2 = 3*2 – 4 is true. Therefore, line l definitely passes through (2,2) and hence statement I is true. As such, answer options B and C cannot be the answers and hence can be eliminated.
Substituting (0,-2) from statement II, we see that -2 = 3*0 -4 is not true. Line l does not pass through (0,-2) and hence statement II is false. Answer option E can be eliminated.
Substituting (-2,-10) from statement III, we see that -10 = 3*(-2) -4 is true. Line l does pass through (-2,-10) and hence statement III is true. Answer option A can be eliminated.
The correct answer option is D.
Hope that helps!
1)If two lines are parallel, their slopes are equal.
2) When the equation of a line is represented in the Slope-Intercept form i.e. the y=mx+c form, the co-efficient of x represents the slope of the line and c represents the y-intercept of the line.
3) When a line passes through a point, the co-ordinates of that point satisfy the equation of the line when substituted.
With this in mind, let us proceed to analyse the question data. The question says that the line l is parallel to the line represented by y=3x + 2. The slope of this line is 3 and the y-intercept is 2. Therefore, the slope of line l should also be 3, but with a different y-intercept.
So, the equation of line l can be written as y = 3x + k, where k is the y-intercept of line l. Since the line passes through (1,-1), the co-ordinates can be substituted in the equation of line l. Doing this,
-1 = 3*1 + k, which yields k= -4 on solving the equation.
Therefore, equation of line l is y=3x – 4. Now that we know the equation of line l, the only thing left out is for us to substitute the co-ordinates of the points given in the statements and see which ones satisfy the equation.
Substituting (2,2) from statement I, we see that 2 = 3*2 – 4 is true. Therefore, line l definitely passes through (2,2) and hence statement I is true. As such, answer options B and C cannot be the answers and hence can be eliminated.
Substituting (0,-2) from statement II, we see that -2 = 3*0 -4 is not true. Line l does not pass through (0,-2) and hence statement II is false. Answer option E can be eliminated.
Substituting (-2,-10) from statement III, we see that -10 = 3*(-2) -4 is true. Line l does pass through (-2,-10) and hence statement III is true. Answer option A can be eliminated.
The correct answer option is D.
Hope that helps!
