In the coordinate system above, which of the following is the equation of line $l?$

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members

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

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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

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Source: Beat The GMAT — Problem Solving | Thu Jan 07, 2021 10:56 am

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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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