GMAT Math : Lines

Study concepts, example questions & explanations for GMAT Math

Create An Account

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #892 : Problem Solving Questions

What is the slope of a line perpendicular to the line of the equation y = 8 ?

Possible Answers:

$-\frac{1}{ 8}$

The line has an undefined slope.

$\frac{1}{ 8}$

Correct answer:

The line has an undefined slope.

Explanation:

The graph of y = b for any real number is a horizontal line. A line parallel to it is a vertical line, which has a slope that is undefined.

Report an Error

Example Question #6 : Calculating The Slope Of A Perpendicular Line

Give the slope of a line on the coordinate plane.

Statement 1: The line shares an -intercept and its -intercept with the line of the equation 5x+7y = 0 .

Statement 2: The line is perpendicular to the line of the equation 5x+7y = 0 .

Possible Answers:

EITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Correct answer:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Explanation:

Assume Statement 1 alone. In order to determine the slope of a line on the coordinate plane, the coordinates of two of its points are needed. The -intercept of the line of the equation can be found by substituting y = 0 and solving for :

5x+7y = 0

5x+7 (0) = 0

5x+0 = 0

5x=0

x = 0

The -intercept of the line is at the origin, (0,0) . It follows that the -intercept is also at the origin. Therefore, Statement 1 only gives one point on the line, and its slope cannot be determined.

Assume Statement 2 alone. The slope of the line of the equation 5x+7y = 0 can be calculated by putting it in slope-intercept form y = mx+b :

5x+7y = 0

5x+7y -5x = 0 -5x

7y = -5x

$7y\div 7 = -5x \div 7$

$y = -\frac{5}{7} x$

The slope of this line is the coefficient of , which is $-\frac{5}{7}$ . A line perpendicular to this one has as its slope the opposite of the reciprocal of $-\frac{5}{7}$ , which is

$- \frac{1}{-\frac{5}{7}} = \frac{7}{5}$ .

The question is answered.

Report an Error

Example Question #61 : Coordinate Geometry

Two perpendicular lines intersect at point (5, Y) . One line passes through (3,7) ; the other, through (10, 4) . What is the value of ?

Possible Answers:

$Y = 3 \textrm{ or }Y=6$

$Y = 2 \textrm{ or }Y=14$

$Y = 2 \textrm{ or }Y=9$

$Y = 1 \textrm{ or }Y=18$

$Y = 4\textrm{ or }Y=7$

Correct answer:

$Y = 2 \textrm{ or }Y=9$

Explanation:

The slope of the first line, in terms of , is

$m_{1} =\frac{Y-7}{5-3} = \frac{Y-7}{2}$

The slope of the second line is

$m_{2} =\frac{Y-4}{5-10} = \frac{Y-4}{-5}$

The slopes of two perpendicular lines have product , so we set up this equation and solve for :

$m_{1}m_{2} = 1$

$\frac{Y-7}{2} \cdot \frac{Y-4}{-5} = -1$

$\frac{ \left ( Y-7 \right ) \left ( Y-4 \right ) }{-10} = -1$

$\left ( Y-7 \right ) \left ( Y-4 \right ) = 10$

$Y ^{2}-11Y + 28 = 10$

$Y ^{2}-11Y + 18 = 0$

$\left ( Y - 2 \right ) \left ( Y - 9 \right ) = 0$

$Y - 2 = 0 \Rightarrow Y = 2$

$Y - 9 = 0 \Rightarrow Y = 9$

Report an Error

Example Question #901 : Gmat Quantitative Reasoning

Which of the following choices give the slopes of two perpendicular lines?

Possible Answers:

-0.8, 1.25

-1.75, 1.75

undefined,

0, -1

3.2, 0.3125

Correct answer:

-0.8, 1.25

Explanation:

We can eliminate the choice 3.2, 0.3125 immediately since the slopes of two perpendicular lines cannot have the same sign. We can also eliminate 0, -1 and undefined, , since a line with slope 0 and a line with undefined slope are perpendicular to each other, not a line of slope -1 or 1.

Of the two remaining choices, we check for the choice that includes two numbers whose product is -1.

$-1.75 \times 1.75 = 3.0625$ and $-0.8 \times 1.25 = -1$

so -0.8, 1.25 is the correct choice.

Report an Error

Example Question #661 : Geometry

Which of the following is perpendicular to the line given by the equation:

$y=\frac{2}{3}x-11$

Possible Answers:

$y=-\frac{2}{3}x+11$

$y=\frac{4}{9}x-13$

$y=\frac{3}{2}x-9$

$y=-\frac{3}{2}x+7$

$y=-\frac{4}{9}x+6$

Correct answer:

$y=-\frac{3}{2}x+7$

Explanation:

In order for one line to be perpendicular to another, its slope must be the negative reciprocal of that line's slope. That is, the slope of any perpendicular line must be opposite in sign and the inverse of the slope of the line to which it is perpendicular:

$m_{perp}=-\frac{1}{m}$

In the given line we can see that $m=\frac{2}{3}$ , so the slope of any line perpendicular to it will be:

$m_{perp}=-\frac{1}{m}=-\frac{1}{\frac{2}{3}}=-\frac{3}{2}$

There is only one answer choice with this slope, so we know the following line is perpendicular to the line given in the problem:

$y=-\frac{3}{2}x+7$

Report an Error

Example Question #61 : Lines

What is the slope of any line that is perpendicular to $y=-\frac{1}{2}x+7$ ?

Possible Answers:

$\frac{1}{2}$

$-\frac{1}{2}$

None of the answers provided

Correct answer:

Explanation:

For a given line defined by the equation y=mx+b with slope , any line perpendicular to has a slope of $-\frac{1}{m}$ , or the negative reciprocal of . Since the slope of the provided line in this instance is $m=-\frac{1}{2}$ , then the slope of any line perpendicular to is $-\frac{1}{m}=-\frac{1}{-\frac{1}{2}}=2$ .

Report an Error

Example Question #904 : Problem Solving Questions

What is the slope of any line that is perpendicular to y=7x+3 ?

Possible Answers:

None of the above

$\frac{1}{7}$

$-\frac{1}{7}$

Correct answer:

$-\frac{1}{7}$

Explanation:

For a given line defined by the equation y=mx+b with slope , any line perpendicular to has a slope of $-\frac{1}{m}$ , or the negative reciprocal of . Since the slope of the provided line in this instance is m=7 , then the slope of any line perpendicular to is $-\frac{1}{m}=-\frac{1}{7}$ .

Report an Error

Example Question #905 : Problem Solving Questions

What is the slope of any line that is perpendicular to $y=\frac{2}{3}x+5$ ?

Possible Answers:

$-\frac{3}{2}$

$\frac{3}{2}$

$-\frac{2}{3}$

$\frac{2}{3}$

None of the above

Correct answer:

$-\frac{3}{2}$

Explanation:

For a given line defined by the equation y=mx+b with slope , any line perpendicular to has a slope of $-\frac{1}{m}$ , or the negative reciprocal of . Since the slope of the provided line in this instance is $m=\frac{2}{3}$ , then the slope of any line perpendicular to is $-\frac{1}{m}=-\frac{1}{\frac{2}{3}}=-\frac{3}{2}$ .

Report an Error

Example Question #61 : Lines

Solve for in the coordinate (3,y) on line 5x+2y=13 ?

Possible Answers:

Correct answer:

Explanation:

To solve for for x=3 , we have to plug into the variable of the equation and solve for :

5(3)+2y=13

15+2y=13

2y=13-15

2y=-2

Report an Error

Example Question #671 : Geometry

Solve for in the coordinate (x,1) on line 3y=4x+1 ?

Possible Answers:

$\frac{1}{2}$

Correct answer:

$\frac{1}{2}$

Explanation:

To solve for for y=1 , we have to plug 1 into the variable of the equation and solve for :

3y=4x+1

3(1)=4x+1

3=4x+1

3-1=4x

2=4x

$x=\frac{1}{2}$

Report an Error

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ISEE Tutors in New York City, Statistics Tutors in Atlanta, Computer Science Tutors in Chicago, Math Tutors in Miami, Reading Tutors in Chicago, Reading Tutors in Phoenix, LSAT Tutors in Houston, GMAT Tutors in Dallas Fort Worth, Biology Tutors in Seattle, Statistics Tutors in Dallas Fort Worth

Popular Courses & Classes

ISEE Courses & Classes in Atlanta, SSAT Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in New York City, GRE Courses & Classes in Seattle, ISEE Courses & Classes in New York City, GMAT Courses & Classes in Los Angeles, LSAT Courses & Classes in Denver, SSAT Courses & Classes in Los Angeles, MCAT Courses & Classes in San Francisco-Bay Area, SAT Courses & Classes in Dallas Fort Worth

Popular Test Prep

MCAT Test Prep in Philadelphia, LSAT Test Prep in Dallas Fort Worth, ISEE Test Prep in Seattle, GMAT Test Prep in Los Angeles, GMAT Test Prep in Atlanta, SSAT Test Prep in Chicago, SSAT Test Prep in Dallas Fort Worth, ISEE Test Prep in Boston, MCAT Test Prep in Atlanta, GMAT Test Prep in Phoenix

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

Email address:
Your name:
Feedback:

GMAT Math : Lines

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #892 : Problem Solving Questions

Example Question #6 : Calculating The Slope Of A Perpendicular Line

Example Question #61 : Coordinate Geometry

Example Question #901 : Gmat Quantitative Reasoning

Example Question #661 : Geometry

Example Question #61 : Lines

Example Question #904 : Problem Solving Questions

Example Question #905 : Problem Solving Questions

Example Question #61 : Lines

Example Question #671 : Geometry

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details