• Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • examPAL
    Most awarded test prep in the world
    Now free for 30 days

    Available with Beat the GMAT members only code

    MORE DETAILS
    examPAL
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT

Find the equation of the line

This topic has 4 expert replies and 1 member reply
GmatGreen Senior | Next Rank: 100 Posts Default Avatar
Joined
31 Mar 2009
Posted:
85 messages

Find the equation of the line

Post Thu Mar 13, 2014 12:28 pm


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

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post Wed Aug 23, 2017 4:53 pm
GmatGreen wrote:

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
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

Cheers,
Brent

_________________
Brent Hanneson – Founder of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

Check out the online reviews of our course
Come see all of our free resources

  • +1 Upvote Post
  • Quote
  • Flag
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!
nikhilgmat31 Legendary Member Default Avatar
Joined
12 May 2015
Posted:
518 messages
Upvotes:
10
Test Date:
3 Oct
Target GMAT Score:
750
Post Tue Jul 28, 2015 11:08 pm
simple way to find the equation with same slope & eliminate others.

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Patrick_GMATFix GMAT Instructor
Joined
21 May 2010
Posted:
1053 messages
Followed by:
98 members
Upvotes:
335
Post Thu Mar 13, 2014 12:40 pm
Equation of the line is y=mx+b where m is the slope and b is the y-intercept. In this case, the slope (change in y / change in x) is -2/3 (calculated from the two known points). The y-intercept (where the line crosses the y-axis is 2. So the equation of the line is y = (-2/3)x + 2. Manipulate it to put x's and y's on the same side and you'll get 2x+3y = 6.

The answer is C. I go through the question in detail in the full solution below (taken from the GMATFix App).



-Patrick

_________________


    Ask me about tutoring.

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post Thu Mar 13, 2014 3:45 pm
GmatGreen wrote:


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
An alternate approach is to PLUG IN THE ANSWERS.
The figure indicates that the following points are on line L: (0,2) and (3,0).
Since a line is defined by two points, only one answer choice can work for both (0,2) and (3,0).

Test (0,2) in the answer choices:
A) 2x - 3y = 6
2*0 - 3*2 = 6.
-6 = 6.
Doesn't work.
Eliminate A.

B) 2x + 3y = 6
2*0 + 3*2 = 6
6 = 6.
This works.

Since (0,2) works in B, test whether (3,0) also works in B:
2*3 + 3*0 = 6
6 = 6.
Success!

The correct answer is B.

_________________
Mitch Hunt
GMAT Private Tutor
GMATGuruNY@gmail.com
If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.
Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.

  • +1 Upvote Post
  • Quote
  • Flag
Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.
Post Tue Jul 28, 2015 1:43 pm
GmatGreen wrote:


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
We start by defining the equation of line l using the slope-intercept form of a line (y = mx + b), where m = slope and b = the y-intercept.

Notice that the two points (0,2) and (3,0) are on line l. We can use these two points to determine the slope. The formula for slope is:

m = (change in y)/(change in x) or

m = (y_2 - y_1)/(x_2 - x_1)

Plugging in our points we have:

m = (0 - 2)/(3 - 0)

m = -2/3

We also see from the diagram that the y-intercept of line l is 2. Substituting the slope and the y-intercept into the line equation we have:

y = (-2/3)x + 2

The final step is to recognize that the answer choices are in a different form than is our equation for line l. Thus, we have to manipulate our equation such that it will match one of the answer choices. Let's first multiply the entire equation by 3. Doing so gives us:

3y = -2x + 6

Then add 2x to both sides of the equation:

2x + 3y = 6

Alternate solution:

To obtain an equation of a line, we can also use the two-intercept form of a line (x/a + y/b = 1) where a is the x-intercept and b is the y-intercept of the line. This is a lesser-known form of an equation of a line, but it comes in handy when we know or are given the x- and y-intercepts of the line. Here, we see that the x-intercept of the line is 3 and the y-intercept is 2. Thus the equation in the two-intercept form is:

x/3 + y/2 = 1

Multiply the entire equation by 6, and we have:

2x + 3y = 6.

The answer is B

_________________
Scott Woodbury-Stewart Founder and CEO

  • +1 Upvote Post
  • Quote
  • Flag

Best Conversation Starters

1 lheiannie07 112 topics
2 ardz24 63 topics
3 LUANDATO 54 topics
4 Roland2rule 52 topics
5 swerve 47 topics
See More Top Beat The GMAT Members...

Most Active Experts

1 image description GMATGuruNY

The Princeton Review Teacher

156 posts
2 image description Scott@TargetTestPrep

Target Test Prep

120 posts
3 image description Jeff@TargetTestPrep

Target Test Prep

106 posts
4 image description EconomistGMATTutor

The Economist GMAT Tutor

92 posts
5 image description Rich.C@EMPOWERgma...

EMPOWERgmat

91 posts
See More Top Beat The GMAT Experts