We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra 1 : How to find out if lines are perpendicular

Study concepts, example questions & explanations for Algebra 1

Create An Account

All Algebra 1 Resources

10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #11 : Perpendicular Lines

Find a line perpendicular to the line with the equation:

$y=\frac{7}{9}x-1$

Possible Answers:

$y=\frac{7}{9}x+6$

$y=-\frac{9}{7}x+9$

$y=\frac{9}{7}x+15$

$y=-\frac{7}{9}x-8$

Correct answer:

$y=-\frac{9}{7}x+9$

Explanation:

Lines can be written in the slope-intercept format:

y=mx+b

In this format, equals the line's slope and represents where the line intercepts the y-axis.

In the given equation:

$m=\frac{7}{9}$

Perpendicular lines have slopes that are negative reciprocals of each other.

First, we need to find its reciprocal.

$\frac{7}{9}\rightarrow\frac{9}{7}$

Second, we need to rewrite it with the opposite sign.

$\frac{9}{7}\rightarrow-\frac{9}{7}$

Only one of the choices has a slope of $-\frac{9}{7}$ .

$y=-\frac{9}{7}x+9$

Report an Error

Example Question #12 : Perpendicular Lines

Find a line perpendicular to the line with the equation:

$y=\frac{5}{2}x-2$

Possible Answers:

y=-5x-7

$y=-\frac{2}{5}x+9$

$y=\frac{2}{5}x+1$

$y=\frac{5}{2}x-8$

Correct answer:

$y=-\frac{2}{5}x+9$

Explanation:

Lines can be written in the slope-intercept format:

y=mx+b

In this format, equals the line's slope and represents where the line intercepts the y-axis.

In the given equation:

$m=\frac{5}{2}$

Perpendicular lines have slopes that are negative reciprocals of each other.

First, we need to find its reciprocal.

$\frac{5}{2}\rightarrow\frac{2}{5}$

Second, we need to rewrite it with the opposite sign.

$\frac{2}{5}\rightarrow-\frac{2}{5}$

Only one of the choices has a slope of $-\frac{2}{5}$ .

$y=-\frac{2}{5}x+9$

Report an Error

Example Question #13 : Perpendicular Lines

Find a line perpendicular to the line with the equation:

$y=-\frac{5}{7}x-61$

Possible Answers:

$y=\frac{7}{5}x+159$

$y=-\frac{7}{5}x-78$

$y=\frac{7}{6}x+78$

$y=\frac{5}{7}x+97$

Correct answer:

$y=\frac{7}{5}x+159$

Explanation:

Lines can be written in the slope-intercept format:

y=mx+b

In this format, equals the line's slope and represents where the line intercepts the y-axis.

In the given equation:

$m=-\frac{5}{7}$

Perpendicular lines have slopes that are negative reciprocals of each other.

First, we need to find its reciprocal.

$-\frac{5}{7}\rightarrow-\frac{7}{5}$

Second, we need to rewrite it with the opposite sign.

$-\frac{7}{5}\rightarrow\frac{7}{5}$

Only one of the choices has a slope of $\frac{7}{5}$ .

$y=\frac{7}{5}x+159$

Report an Error

Example Question #14 : Perpendicular Lines

Find a line perpendicular to the line with the equation:

$y=\frac{3}{4}x-23$

Possible Answers:

$y=-\frac{3}{4}x+84$

$y=\frac{4}{3}x-88$

$y=\frac{3}{4}x+56$

$y=-\frac{4}{3}x+87$

Correct answer:

$y=-\frac{4}{3}x+87$

Explanation:

Lines can be written in the slope-intercept format:

y=mx+b

In this format, equals the line's slope and represents where the line intercepts the y-axis.

In the given equation:

$m=\frac{3}{4}$

Perpendicular lines have slopes that are negative reciprocals of each other.

First, we need to find its reciprocal.

$\frac{3}{4}\rightarrow\frac{4}{3}$

Second, we need to rewrite it with the opposite sign.

$\frac{4}{3}\rightarrow-\frac{4}{3}$

Only one of the choices has a slope of $-\frac{4}{3}$ .

$y=-\frac{4}{3}x+87$

Report an Error

Example Question #15 : Perpendicular Lines

Find a line perpendicular to the line with the equation:

y=2x-10

Possible Answers:

y=-2x+2

y=2x+2

$y=-\frac{1}{2}$

$y=-\frac{1}{2}x+2$

Correct answer:

$y=-\frac{1}{2}x+2$

Explanation:

Lines can be written in the slope-intercept format:

y=mx+b

In this format, equals the line's slope and represents where the line intercepts the y-axis.

In the given equation:

m=2

Perpendicular lines have slopes that are negative reciprocals of each other.

First, we need to find its reciprocal.

$2\rightarrow\frac{1}{2}$

Second, we need to rewrite it with the opposite sign.

$\frac{1}{2}\rightarrow-\frac{1}{2}$

Only one of the choices has a slope of $-\frac{1}{2}$ .

$y=-\frac{1}{2}x+2$

Report an Error

Example Question #16 : Perpendicular Lines

Find a line perpendicular to the line with the equation:

$y=-5x+\frac{1}{5}$

Possible Answers:

$y=-\frac{1}{5}x-8$

y=5x+2

y=-5x+5

$y=\frac{1}{5}x-5$

Correct answer:

$y=\frac{1}{5}x-5$

Explanation:

Lines can be written in the slope-intercept format:

y=mx+b

In this format, equals the line's slope and represents where the line intercepts the y-axis.

In the given equation:

m=-5

Perpendicular lines have slopes that are negative reciprocals of each other.

First, we need to find its reciprocal.

$-5\rightarrow-\frac{1}{5}$

Second, we need to rewrite it with the opposite sign.

$-\frac{1}{5}\rightarrow\frac{1}{5}$

Only one of the choices has a slope of $\frac{1}{5}$ .

$y=\frac{1}{5}x-5$

Report an Error

Example Question #17 : Perpendicular Lines

Find a line perpendicular to the line with the equation:

$y=\frac{3}{10}x-9$

Possible Answers:

$y=\frac{3}{10}x+100$

$y=-\frac{10}{3}x+98$

$y=\frac{10}{3}x+100$

$y=-\frac{3}{10}x-78$

Correct answer:

$y=-\frac{10}{3}x+98$

Explanation:

Lines can be written in the slope-intercept format:

y=mx+b

In this format, equals the line's slope and represents where the line intercepts the y-axis.

In the given equation:

$m=\frac{3}{10}$

Perpendicular lines have slopes that are negative reciprocals of each other.

First, we need to find its reciprocal.

$\frac{3}{10}\rightarrow\frac{10}{3}$

Second, we need to rewrite it with the opposite sign.

$\frac{10}{3}\rightarrow-\frac{10}{3}$

Only one of the choices has a slope of $-\frac{10}{3}$ .

$y=-\frac{10}{3}x+98$

Report an Error

Example Question #18 : Perpendicular Lines

Find a line perpendicular to the line with the equation:

y=100x-2

Possible Answers:

y=-102x-2

$y=-\frac{1}{100}x+85$

$y=\frac{1}{100}x+55$

y=100x+102

Correct answer:

$y=-\frac{1}{100}x+85$

Explanation:

Lines can be written in the slope-intercept format:

y=mx+b

In this format, equals the line's slope and represents where the line intercepts the y-axis.

In the given equation:

m=100

Perpendicular lines have slopes that are negative reciprocals of each other.

First, we need to find its reciprocal.

$100\rightarrow\frac{1}{100}$

Second, we need to rewrite it with the opposite sign.

$\frac{1}{100}\rightarrow-\frac{1}{100}$

Only one of the choices has a slope of $-\frac{1}{100}$ .

$y=-\frac{1}{100}x+85$

Report an Error

Example Question #11 : How To Find Out If Lines Are Perpendicular

Given the two lines: y=2x and $y= -\frac{1}{2}x$ , are the lines perpendicular to each other?

Possible Answers:

$\textup{No, the slopes are not negative reciprocals of each other.}$

$\textup{No, because the slopes have no y-intercept.}$

$\textup{Yes, because both lines are in slope-intercept form.}$

$\textup{No, the slopes must be the same for both lines.}$

$\textup{Yes, the slopes are negative reciprocals of each other.}$

Correct answer:

$\textup{Yes, the slopes are negative reciprocals of each other.}$

Explanation:

Write the perpendicular line slope formula. The perpendicular slope is the negative reciprocal of the original slope.

$m_{perpendicular} = -\frac{1}{m_{original}}$

Let y=2x be the original equation. The slope is . Substitute this into the equation to find the slope of any perpendicular line.

$m_{perpendicular} = -\frac{1}{2}$

The slope of a perpendicular line must have a slope of $-\frac{1}{2}$ , which is also the slope for $y= -\frac{1}{2}x$ .

The answer is:

$\textup{Yes, the slopes are negative reciprocal to each other.}$

Report an Error

Example Question #3541 : Algebra 1

Select the equation of the line that is perpendicular to $y=\frac{1}{2}x-4$ .

Possible Answers:

None of the other answers.

y=-2x+3

$y=-\frac{1}{2}x+3$

y=2x+3

y=2x-4

Correct answer:

y=-2x+3

Explanation:

Lines are perpendicular if their slopes are negative reciprocals of one another. For example, the negative reciprocal of $3=-\frac{1}{3}$ . So y=-2x+3 is perpendicular to $y=\frac{1}{2}x-4$ because their slopes are the negative reciprocals of each other. $\frac{1}{2}=-2\hspace{1mm}and\hspace{1mm} -2=-\frac{1}{-2}=\frac{1}{2}$ . A positive slope can still be the negative reciprocal as you can see.

Report an Error

View Algebra Tutors

Dejuan
Certified Tutor

University of Illinois at Urbana-Champaign, Bachelor of Science, Electrical Engineering.

View Algebra Tutors

Yucheng
Certified Tutor

The University of Texas at Austin, Bachelor of Science, Mechanical Engineering.

View Algebra Tutors

Dilip
Certified Tutor

University of Calcutta, Bachelor of Science, Physics. Indiana Institute of Technology, Master of Science, Physics.

All Algebra 1 Resources

10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Math Tutors in Boston, GMAT Tutors in San Francisco-Bay Area, GRE Tutors in Denver, GRE Tutors in San Diego, Statistics Tutors in Miami, Reading Tutors in Seattle, Statistics Tutors in Houston, Biology Tutors in San Diego, Physics Tutors in Boston, MCAT Tutors in Atlanta

Popular Courses & Classes

ACT Courses & Classes in San Diego, ISEE Courses & Classes in New York City, ISEE Courses & Classes in Denver, ACT Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in San Diego, LSAT Courses & Classes in Atlanta, MCAT Courses & Classes in Phoenix, GMAT Courses & Classes in New York City, Spanish Courses & Classes in New York City, LSAT Courses & Classes in San Francisco-Bay Area

Popular Test Prep

LSAT Test Prep in Philadelphia, GMAT Test Prep in Chicago, GRE Test Prep in San Diego, MCAT Test Prep in Seattle, MCAT Test Prep in New York City, GRE Test Prep in Washington DC, ISEE Test Prep in New York City, LSAT Test Prep in Houston, ISEE Test Prep in Phoenix, SSAT Test Prep in Philadelphia

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)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Algebra 1 : How to find out if lines are perpendicular

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #11 : Perpendicular Lines

Example Question #12 : Perpendicular Lines

Example Question #13 : Perpendicular Lines

Example Question #14 : Perpendicular Lines

Example Question #15 : Perpendicular Lines

Example Question #16 : Perpendicular Lines

Example Question #17 : Perpendicular Lines

Example Question #18 : Perpendicular Lines

Example Question #11 : How To Find Out If Lines Are Perpendicular

Example Question #3541 : Algebra 1

All Algebra 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: