GRE Math : Other Lines

Study concepts, example questions & explanations for GRE Math

Create An Account

All GRE Math Resources

13 Diagnostic Tests 452 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #243 : Geometry

What is the equation of a line passing through the two points (41,11) and (4,-9) ?

Possible Answers:

$y=\frac{20}{27}x-\frac{14}{15}$

y=14x-18

$y=\frac{17}{14}x-\frac{148}{25}$

$y=\frac{20}{37}x-\frac{413}{37}$

$y=\frac{7}{2}x-\frac{85}{3}$

Correct answer:

$y=\frac{20}{37}x-\frac{413}{37}$

Explanation:

Based on the information provided, you can find the slope of this line easily. From that, you can use the point-slope form of the equation of a line to compute the line's full equation. The slope is merely:

$\frac{rise}{run}=\frac{11-(-9)}{41-4}=\frac{11+9}{37}=\frac{20}{37}$

Now, for a point (a,b) and a slope , the point-slope form of a line is:

y-b=m(x-a)

Let's use (4,-9) for our point (a,b)

This gives us:

$y+9=\frac{20}{37}(x-4)$

Now, distribute and solve for :

$y+9=\frac{20}{37}x-\frac{80}{37}$

$y=\frac{20}{37}x-\frac{80}{37}-9$

$y=\frac{20}{37}x-\frac{80}{37}-\frac{333}{37}$

$y=\frac{20}{37}x-\frac{413}{37}$

Report an Error

Example Question #243 : Geometry

What is the equation of a line passing through (4,-12) with a -intercept of ?

Possible Answers:

y=-5x-9

$y=\frac{-15}{4}x+12$

$y=\frac{27}{5}x+9$

y=-22x+15

$y=\frac{-21}{4}x+9$

Correct answer:

$y=\frac{-21}{4}x+9$

Explanation:

Based on the information that you have been provided, you can quickly find the slope of your line. Since the y-intercept is , you know that the line contains the point (0,9) . Therefore, the slope of the line is found:

$\frac{-12-9}{4-0}=\frac{-21}{4}$

Based on this information, you can use the standard slope-intercept form to find your equation:

y=mx+b , where $m=\frac{-21}{4}$ and b=9

$y=\frac{-21}{4}x+9$

Report an Error

Example Question #244 : Geometry

Given the graph of the line below, find the equation of the line.

Act_math_160_04

Possible Answers:

$y=\frac{10}{3}x-4$

y=-x

y=-5x-4

y=x-4

Correct answer:

$y=\frac{10}{3}x-4$

Explanation:

To solve this question, you could use two points such as (1.2,0) and (0,-4) to calculate the slope which is 10/3 and then read the y-intercept off the graph, which is -4.

Report an Error

Example Question #111 : Algebra

Which line passes through the points (0, 6) and (4, 0)?

Possible Answers:

y = 1/5x + 3

y = 2/3x –6

y = –3/2x + 6

y = –3/2 – 3

y = 2/3 + 5

Correct answer:

y = –3/2x + 6

Explanation:

P₁ (0, 6) and P₂ (4, 0)

First, calculate the slope: m = rise ÷ run = (y₂ – y₁)/(x₂– x₁), so m = –3/2

Second, plug the slope and one point into the slope-intercept formula:

y = mx + b, so 0 = –3/2(4) + b and b = 6

Thus, y = –3/2x + 6

Report an Error

Example Question #278 : Ssat Upper Level Quantitative (Math)

What line goes through the points (1, 3) and (3, 6)?

Possible Answers:

4x – 5y = 4

3x + 5y = 2

–3x + 2y = 3

2x – 3y = 5

–2x + 2y = 3

Correct answer:

–3x + 2y = 3

Explanation:

If P₁(1, 3) and P₂(3, 6), then calculate the slope by m = rise/run = (y₂ – y₁)/(x₂ – x₁) = 3/2

Use the slope and one point to calculate the intercept using y = mx + b

Then convert the slope-intercept form into standard form.

Report an Error

Example Question #1 : Other Lines

What is the slope-intercept form of $\dpi{100} \small 8x-2y-12=0$ ?

Possible Answers:

$\dpi{100} \small y=-2x+3$

$\dpi{100} \small y=-4x+6$

$\dpi{100} \small y=2x-3$

$\dpi{100} \small y=4x-6$

$\dpi{100} \small y=4x+6$

Correct answer:

$\dpi{100} \small y=4x-6$

Explanation:

The slope intercept form states that $\dpi{100} \small y=mx+b$ . In order to convert the equation to the slope intercept form, isolate $\dpi{100} \small y$ on the left side:

$\dpi{100} \small 8x-2y=12$

$\dpi{100} \small -2y=-8x+12$

$\dpi{100} \small y=4x-6$

Report an Error

Example Question #2 : How To Find The Equation Of A Line

A line is defined by the following equation:

7x+28y=84

What is the slope of that line?

Possible Answers:

$\frac{1}{4}$

$-\frac{1}{4}$

Correct answer:

$-\frac{1}{4}$

Explanation:

The equation of a line is

y=mx + b where m is the slope

Rearrange the equation to match this:

7x + 28y = 84

28y = -7x + 84

y = -(7/28)x + 84/28

y = -(1/4)x + 3

m = -1/4

Report an Error

Example Question #731 : Act Math

If the coordinates (3, 14) and (–5, 15) are on the same line, what is the equation of the line?

Possible Answers:

$y=\frac{1}{8}x+14.375$

$y=-\frac{1}{8}x+14.375$

y=-8x-38

y=-8x+38

$y=-\frac{1}{8}x+13.625$

Correct answer:

$y=-\frac{1}{8}x+14.375$

Explanation:

First solve for the slope of the line, m using y=mx+b

m = (y2 – y1) / (x2 – x1)

= (15 – 14) / (–5 –3)

= (1 )/( –8)

=–1/8

y = –(1/8)x + b

Now, choose one of the coordinates and solve for b:

14 = –(1/8)3 + b

14 = –3/8 + b

b = 14 + (3/8)

b = 14.375

y = –(1/8)x + 14.375

Report an Error

Example Question #1 : Coordinate Geometry

What is the equation of a line that passes through coordinates $\dpi{100} \small (2,6)$ and $\dpi{100} \small (3,5)$ ?

Possible Answers:

$\dpi{100} \small y=3x+2$

$\dpi{100} \small y=-x+8$

$\dpi{100} \small y=2x-4$

$\dpi{100} \small y=x+7$

$\dpi{100} \small y=2x+4$

Correct answer:

$\dpi{100} \small y=-x+8$

Explanation:

Our first step will be to determing the slope of the line that connects the given points.

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{6-5}{2-3}=\frac{1}{-1}=-1$

Our slope will be . Using slope-intercept form, our equation will be y=(-1)x+b . Use one of the give points in this equation to solve for the y-intercept. We will use $\dpi{100} \small (2,6)$ .

6=(-1)(2)+b

6=-2+b

8=b

Now that we know the y-intercept, we can plug it back into the slope-intercept formula with the slope that we found earlier.

y=(-1)x+8

y=-x+8

This is our final answer.

Report an Error

Example Question #1 : How To Find The Equation Of A Line

Which of the following equations does NOT represent a line?

Possible Answers:

x-y=10

5y=10

x^2+y=10

x+y=10

x=10

Correct answer:

x^2+y=10

Explanation:

The answer is x^2+y=10 .

A line can only be represented in the form x=z or y=mx+b , for appropriate constants , , and . A graph must have an equation that can be put into one of these forms to be a line.

x^2+y=10 represents a parabola, not a line. Lines will never contain an x^2 term.

Report an Error

All GRE Math Resources

13 Diagnostic Tests 452 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

MCAT Tutors in Los Angeles, GMAT Tutors in New York City, Algebra Tutors in Atlanta, Biology Tutors in Miami, Algebra Tutors in Philadelphia, Computer Science Tutors in Denver, Algebra Tutors in Seattle, SAT Tutors in Chicago, Computer Science Tutors in Atlanta, GMAT Tutors in Phoenix

Popular Courses & Classes

MCAT Courses & Classes in New York City, Spanish Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Seattle, SSAT Courses & Classes in San Francisco-Bay Area, SAT Courses & Classes in New York City, GRE Courses & Classes in Houston, ACT Courses & Classes in San Diego, Spanish Courses & Classes in Washington DC, ACT Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in New York City

Popular Test Prep

GMAT Test Prep in San Diego, ISEE Test Prep in Denver, SAT Test Prep in San Francisco-Bay Area, GMAT Test Prep in Chicago, SAT Test Prep in Boston, GRE Test Prep in Atlanta, ACT Test Prep in Dallas Fort Worth, GRE Test Prep in Miami, GRE Test Prep in San Francisco-Bay Area, SSAT Test Prep in Chicago

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:

GRE Math : Other Lines

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #243 : Geometry

Example Question #243 : Geometry

Example Question #244 : Geometry

Example Question #111 : Algebra

Example Question #278 : Ssat Upper Level Quantitative (Math)

Example Question #1 : Other Lines

Example Question #2 : How To Find The Equation Of A Line

Example Question #731 : Act Math

Example Question #1 : Coordinate Geometry

Example Question #1 : How To Find The Equation Of A Line

All GRE Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details