We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

SAT Math : How to find slope of a line

Study concepts, example questions & explanations for SAT Math

Create An Account

All SAT Math Resources

16 Diagnostic Tests 660 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #511 : Geometry

A line passes through the origin, and the points (1, k) and (k,4). What is a possible value for k?

Possible Answers:

k=-4

k=2

k=1

k=4

k=0

Correct answer:

k=2

Explanation:

To find k, first identify what is known.

The origin means the point (0,0).

Therefore the line passes through the points:

(0,0), (1,k),(k,4)

Since a line by definition has the same slope between the points, calculation the slope between the origin and each of the points.

$\text{slope}=\frac{y_2-y_1}{x_2-x_1}$

Let

$\\(x_1,y_1)=(0,0) \\(x_2,y_2)=(1,k)$

therefore the slope is,

$\text{slope}=\frac{k-0}{1-0}=k$

Now let,

$\\(x_1,y_1)=(0,0) \\(x_2,y_2)=(k,4)$

thus the slope is,

$\text{slope}=\frac{4-0}{k-0}=\frac{4}{k}$

From here set the slopes equal to each other and solve for k.

$k=\frac{4}{k}$

Multiply by k on both sides.

$\\k\cdot k=\frac{4}{k}\cdot k \\\\k^2=4 \\\\\sqrt{k^2}=\sqrt{4} \\\\k=\pm2$

Report an Error

Example Question #512 : Sat Mathematics

Axes

Figure NOT drawn to scale

On the coordinate axes shown above, the shaded triangle has area 60.

Give the slope of the line that includes the hypotenuse of the triangle.

Possible Answers:

$- \frac{12}{5}$

$- \frac{5}{12}$

$- \frac{6}{5}$

$- \frac{5}{6}$

$\textup{None of the other choices gives the correct response}$

Correct answer:

$- \frac{6}{5}$

Explanation:

The length of the vertical leg of the triangle is the distance from the origin (0,0) to (0, 12) , which is 12.

The area of a right triangle is half the product of the lengths of its legs and , so, setting b= 12 and A = 60 and solving for :

$\frac{1}{2} ab = A$

$\frac{1}{2} \cdot a \cdot 12 = 60$

6a = 60

$\frac{6a }{6}= \frac{60}{6}$

a= 10

Since this is the positive horizontal distance from the origin, this is also the -coordinate of the -intercept of the line - that is, the line has -intercept (10,0) .

The slope of a line, given the intercepts (a,0) , (0, b) , is

$m = - \frac{b}{a}$ ,

Substitute a= 10 and :

$m = - \frac{12}{10} = - \frac{6}{5}$

Report an Error

View SAT Mathematics Tutors

Momeena
Certified Tutor

State University of New York at New Paltz, Bachelors, Mathematics & Elementary Education. State University of New York at New...

View SAT Mathematics Tutors

Stephen
Certified Tutor

Grinnell College, Bachelor in Arts, Computer Science.

View SAT Mathematics Tutors

Scott
Certified Tutor

Rutgers College, Bachelors, Political Science and Government. Florida Coastal School of Law, PHD, Law.

All SAT Math Resources

16 Diagnostic Tests 660 Practice Tests Question of the Day Flashcards Learn by Concept

SAT Math Tutors in Top Cities:

Atlanta SAT Math Tutors, Austin SAT Math Tutors, Boston SAT Math Tutors, Chicago SAT Math Tutors, Dallas Fort Worth SAT Math Tutors, Denver SAT Math Tutors, Houston SAT Math Tutors, Kansas City SAT Math Tutors, Los Angeles SAT Math Tutors, Miami SAT Math Tutors, New York City SAT Math Tutors, Philadelphia SAT Math Tutors, Phoenix SAT Math Tutors, San Diego SAT Math Tutors, San Francisco-Bay Area SAT Math Tutors, Seattle SAT Math Tutors, St. Louis SAT Math Tutors, Tucson SAT Math Tutors, Washington DC SAT Math Tutors

Popular Courses & Classes

SSAT Courses & Classes in San Diego, GRE Courses & Classes in Phoenix, SAT Courses & Classes in Miami, Spanish Courses & Classes in San Diego, MCAT Courses & Classes in Seattle, Spanish Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in Chicago, SAT Courses & Classes in Phoenix, GRE Courses & Classes in Chicago, SAT Courses & Classes in Chicago

Popular Test Prep

LSAT Test Prep in Boston, ISEE Test Prep in Philadelphia, MCAT Test Prep in Atlanta, SAT Test Prep in Houston, GRE Test Prep in Phoenix, MCAT Test Prep in Dallas Fort Worth, SAT Test Prep in Philadelphia, SSAT Test Prep in Denver, ISEE Test Prep in Washington DC, ACT Test Prep in San Diego

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

SAT Math : How to find slope of a line

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #511 : Geometry

Example Question #512 : Sat Mathematics

All SAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: