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In the coordinate system above, which of the following is the equation of line \(l?\)

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In the coordinate system above, which of the following is the equation of line \(l?\)

by Gmat_mission » Thu Jan 07, 2021 10:56 am

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In the coordinate system above, which of the following is the equation of line \(l?\)

(A) \(2x - 3y = 6\)
(B) \(2x + 3y = 6\)
(C) \(3x + 2y = 6\)
(D) \(2x - 3y = -6\)
(E) \(3x - 2y = -6\)

Answer: B

Source: Official Guide
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Re: In the coordinate system above, which of the following is the equation of line \(l?\)

by Brent@GMATPrepNow » Mon Jan 11, 2021 7:39 am
Gmat_mission wrote: ↑
Thu Jan 07, 2021 10:56 am
 Line L.png

In the coordinate system above, which of the following is the equation of line \(l?\)

(A) \(2x - 3y = 6\)
(B) \(2x + 3y = 6\)
(C) \(3x + 2y = 6\)
(D) \(2x - 3y = -6\)
(E) \(3x - 2y = -6\)

Answer: B

Source: Official Guide
We can see that points (0,2) and (3,0) are ON THE LINE. So, their coordinates must SATISFY the equation of the line.

Let's start with (0,2).
(A) 2x - 3y = 6. 2(0) - 3(2) = -6 ELIMINATE
(B) 2x + 3y = 6. 2(0) + 3(2) = 6 KEEP
(C) 3x + 2y = 6. 3(0) +2(2) = 4 ELIMINATE
(D) 2x - 3y = -6. 2(0) - 3(2) = -6 KEEP
(E) 3x - 2y = -6. 3(0) - 2(2) = -4 ELIMINATE

Great. We're down to B or D

Let's test (3,0).
(B) 2x + 3y = 6. 2(3) + 3(0) = 6 KEEP
(D) 2x - 3y = -6. 2(3) - 3(0) = 6 ELIMINATE

Answer: B
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Re: In the coordinate system above, which of the following is the equation of line \(l?\)

by Scott@TargetTestPrep » Tue Jan 19, 2021 7:38 am
Gmat_mission wrote: ↑
Thu Jan 07, 2021 10:56 am
 Line L.png

In the coordinate system above, which of the following is the equation of line \(l?\)

(A) \(2x - 3y = 6\)
(B) \(2x + 3y = 6\)
(C) \(3x + 2y = 6\)
(D) \(2x - 3y = -6\)
(E) \(3x - 2y = -6\)

Answer: B

Source: Official Guide
Solution:

We see that the two intercepts are 3 (the x-intercept) and 2 (the y-intercept). Both of these should satisfy the equation of line ℓ. Looking at the given choices, we see that choice B is the correct answer since 2(3) + 3(0) = 6 (when we substitute the values of x and y for the coordinates of the x-intercept) and 2(0) + 3(2) = 6 (when we substitute the values of x and y for the coordinates of the y-intercept).

Answer: B

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