Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Notice that line l passes through points (3,0) and (0,2), so its slope is \(m=\frac{y_2-y_1}{x_2-x_1}=-\frac{2}{3}\) (given two points \((x_1,y_1)\) and \((x_2,y_2)\) on a line, the slope \(m\) of the line is \(m=\frac{y_2-y_1}{x_2-x_1}\)).

Only option B, when written in \(y=mx+b\) form has the slope of -2/3.

Notice that line l passes through points (3,0) and (0,2), so its slope is \(m=\frac{y_2-y_1}{x_2-x_1}=-\frac{2}{3}\) (given two points \((x_1,y_1)\) and \((x_2,y_2)\) on a line, the slope \(m\) of the line is \(m=\frac{y_2-y_1}{x_2-x_1}\)).

Only option B, when written in \(y=mx+b\) form has the slope of -2/3.

Answer: B.

Hi Bunnel...A small query Can we assume (As u have done in your solution) that the line passes through points (3,0) and (0,2). I mean can we safely interpret graphs on the GMAT??Since it is not explicitly stated that the line passes through those two specific points. My approach to the above problem was as follows. What we know from the graph is this x and y co-ordinates of line l are both positive, x co-ordinate is > 2 and y co-ordinate is > 1 Checking answer choices - A, D and E are clearly out since x and y co-ordinates will have opposite signs putting y=0 in choice C x=2 - Incorrect (as x co-ordinate > 2) Only B left Cheers

Notice that line l passes through points (3,0) and (0,2), so its slope is \(m=\frac{y_2-y_1}{x_2-x_1}=-\frac{2}{3}\) (given two points \((x_1,y_1)\) and \((x_2,y_2)\) on a line, the slope \(m\) of the line is \(m=\frac{y_2-y_1}{x_2-x_1}\)).

Only option B, when written in \(y=mx+b\) form has the slope of -2/3.

Answer: B.

Hi Bunnel...A small query Can we assume (As u have done in your solution) that the line passes through points (3,0) and (0,2). I mean can we safely interpret graphs on the GMAT??Since it is not explicitly stated that the line passes through those two specific points. My approach to the above problem was as follows. What we know from the graph is this x and y co-ordinates of line l are both positive, x co-ordinate is > 2 and y co-ordinate is > 1 Checking answer choices - A, D and E are clearly out since x and y co-ordinates will have opposite signs putting y=0 in choice C x=2 - Incorrect (as x co-ordinate > 2) Only B left Cheers

OG13 solution makes the same exact assumption "The line is shown going through the points (0,2) and (3,0)..."
_________________

From the given figure, we can see that the line has positive intercept on both the x and y axis. Thus we can eliminate all the options except B and C. Now the intercept on the x-axis is more than 2. For option C, the x-intercept comes as 2, thus the answer has to be B.
_________________

Re: In the coordinate system above, which of the following is the equation [#permalink]

Show Tags

07 Nov 2013, 22:41

Just a different way of approaching the problem... since we know the y-intercept is -c/b when the equation is given in the form ax+by +c =0.. simply use what's on the right side of the equation (it'll turn negative when moved to the left) and divide by b.

Notice that line l passes through points (3,0) and (0,2), so its slope is \(m=\frac{y_2-y_1}{x_2-x_1}=-\frac{2}{3}\) (given two points \((x_1,y_1)\) and \((x_2,y_2)\) on a line, the slope \(m\) of the line is \(m=\frac{y_2-y_1}{x_2-x_1}\)).

Only option B, when written in \(y=mx+b\) form has the slope of -2/3.

Answer: B.

Hi Bunnel...A small query Can we assume (As u have done in your solution) that the line passes through points (3,0) and (0,2). I mean can we safely interpret graphs on the GMAT??Since it is not explicitly stated that the line passes through those two specific points. My approach to the above problem was as follows. What we know from the graph is this x and y co-ordinates of line l are both positive, x co-ordinate is > 2 and y co-ordinate is > 1 Checking answer choices - A, D and E are clearly out since x and y co-ordinates will have opposite signs putting y=0 in choice C x=2 - Incorrect (as x co-ordinate > 2) Only B left Cheers

OG13 solution makes the same exact assumption "The line is shown going through the points (0,2) and (3,0)..."

I agree with Dipankar6435 approach. I used the similar approach since it is not explicitly mentioned that the line passes through and also there is no line markers at the points where the line touches both x and y axis. Since there is a line marker on the x axis that clearly indicates that the x value should be greater than 2, out of the 2 answer choices, I picked B as the right one. Thanks.

Notice that line l passes through points (3,0) and (0,2), so its slope is \(m=\frac{y_2-y_1}{x_2-x_1}=-\frac{2}{3}\) (given two points \((x_1,y_1)\) and \((x_2,y_2)\) on a line, the slope \(m\) of the line is \(m=\frac{y_2-y_1}{x_2-x_1}\)).

Only option B, when written in \(y=mx+b\) form has the slope of -2/3.

Answer: B.

Hi Bunnel...A small query Can we assume (As u have done in your solution) that the line passes through points (3,0) and (0,2). I mean can we safely interpret graphs on the GMAT??Since it is not explicitly stated that the line passes through those two specific points. My approach to the above problem was as follows. What we know from the graph is this x and y co-ordinates of line l are both positive, x co-ordinate is > 2 and y co-ordinate is > 1 Checking answer choices - A, D and E are clearly out since x and y co-ordinates will have opposite signs putting y=0 in choice C x=2 - Incorrect (as x co-ordinate > 2) Only B left Cheers

OG13 solution makes the same exact assumption "The line is shown going through the points (0,2) and (3,0)..."

Very very strange because in Maths , one is groomed to never make assumptions based on diagrams unless explicitly mentioned .

Re: In the coordinate system above, which of the following is the equation [#permalink]

Show Tags

17 May 2014, 05:11

1

This post was BOOKMARKED

There is another general form of line in co-ordinate plane which is:

x/a + y/b = 1

where a is the point of intersection of line and x-axis and b is the point of intersection of line with y-axis. Here a=3, b=2 Therefore,

x/3 + y/2 = 1

or

2x + 3y = 6

This solution is valid, if we assume the values of a, and b.

But even if we don’t assume these values, we can eliminate option A), D), and E) because, we can see that both the x intercept and y intercept are positive.

Now, we see a>b through observation, which means coefficient of x is greater than coefficient of y, which is in option B) only. Hence B is the answer.

Re: In the coordinate system above, which of the following is the equation [#permalink]

Show Tags

21 May 2014, 03:59

1

This post received KUDOS

If intercept on the x axis and y axis is known, intercept formula for line is the fastest method to get the equation of the line.

Equation of a line which cut an intercept a at x axis and b at y axis is given by

(x/a) + (y/b) = 1

However, a more useful form of this equation is

bx + ay = ab

using this, equation of line can be found easily by inspection only Here , Intercept at x axis = a = 3 Intercept at y axis = b = 2 hence, equation of line by putting values 2x+3y =6 hence answer is B
_________________

Without any calculation Approach! We know from the graph that X-intercept must be greater than 2. So, co-efficient of x must be 2. Hence C and E are out. The equation of straight line is y=mx+b and In the figure we can see that slope must be negative. Therefore, A and D are out since they have positive slope. Answer is B.

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 line l has two points: (0,2) and (3,0). 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. This gives us:

3y = -2x + 6

Then add 2x to both sides of the equation:

2x + 3y = 6

The answer is B.
_________________

Jeffery Miller Head of GMAT Instruction

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

A very simple approach would be - Notice line l has a negative slope and the line l intersects in 0,2 and 3,0. Only option B & C satisfies i.e they have a negative slope { rewrite them in slope intercept form y= mx + b}

B. y = -2/3x + 2 { put the points 0,2 & 3,0 - they both satisfies the equation} C. y = -3/2x + 2 { put the points 0,2 & 3,0- notice 3,0 doesn't satisfies the equation}.

Hope you understood. Please press the kudos for the appreciation.

-------- Equation of a line can be writter as (x/a) + (y/b) =1 where a = x intercept & b=y intercept from figure both a & b are + ve => only options B & C remain

And again from figure a>b => option B is the best possible choice