Call Now to Set Up Tutoring:

(888) 888-0446

Intermediate Geometry : Other Lines

Study concepts, example questions & explanations for Intermediate Geometry

Create An Account

All Intermediate Geometry Resources

8 Diagnostic Tests 250 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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

What is the equation of a line with a slope of and an -intercept of ?

Possible Answers:

y=2x+4

y=2x+2

$y=\frac{1}{2}x +4$

y=2x-4

y=2x-2

Correct answer:

y=2x-4

Explanation:

The -intercept is the value of when the value is equal to zero. The actual point located on the graph for an -intercept of is (2,0) . The slope, , is 2.

Write the slope-intercept equation and substitute the point and slope to solve for the -intercept:

y=mx+b

0=2(2)+b

b=-4

Plug the slope and -intercept back in the slope-intercept formula:

y=2x-4

Report an Error

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

A line goes through the following points (2,3) and (3, 7) .

Find the equation of the line.

Possible Answers:

$y=\frac{1}{4}x+5$

y=4x+13

y=4x-5

y=4x+5

$y=\frac{1}{4}x-13$

Correct answer:

y=4x-5

Explanation:

First, find the slope of the line using the slope formula:

$\frac{y_2-y_1}{x_2-x_1}=\frac{7-3}{3-2}=\frac{4}{1}=4$ .

Next we plug one of the points, and the slope, into the point-intercept line forumula:

y=mx+b where m is our slope.

Then y=4x+b and when we plug in point (2,3) the formula reads 3=4(2)+b then solve for b.

3-8=-5 =b .

To find the equation of the line, we plug in our m and b into the slope-intercept equation.

So, y=4x+(-5) or simplified, y=4x-5 .

Report an Error

Example Question #4 : How To Find The Equation Of A Line

Write the equation for the line passing through the points (4,-1) and (-4, 3)

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

To determine the equation, first find the slope:

$\frac{\Delta y}{\Delta x} = \frac{3--1}{-4-4} = \frac{4 }{-8 } =- \frac{1}{2}$

We want this equation in slope-intercept form, y = mx+b . We know and because we have two coordinate pairs to choose from representing an and a . We know because that represents the slope. We just need to solve for , and then we can write the equation.

We can choose either point and get the correct answer. Let's choose (4, -1) :

$-1 = -\frac{1}{2} (4) + b$ multiply ""

-1 = -2 + b add to both sides

1 = b

This means that the y = mx+b form is $y = -\frac{1}{2}x +1$

Report an Error

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

Write the equation for a line that passes through the points (3,2) and (2,-1) .

Possible Answers:

y = x-3

$y = \frac{1}{3}x - 13$

y = x + 1

y = 5x -13

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

Correct answer:

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

Explanation:

To determine the equation, first find the slope:

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

We can choose either point and get the correct answer. Let's choose (3,2) :

$2= \frac{1}{3} (3) + b$ multiply ""

2 = 1 + b subtract from both sides

1 = b

This means that the y = mx+b form is $y = \frac{1}{3}x +1$

Report an Error

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

Find the equation for a line passing through the points (5, -1) and (3,-7) .

Possible Answers:

y = 3x + 2

$y = \frac{1}{3}x -6$

y = 3x-16

$y = \frac{1}{3} x -8$

y = -3x +14

Correct answer:

y = 3x-16

Explanation:

To determine the equation, first find the slope:

$\frac{\Delta y}{\Delta x} = \frac{-7--1}{3-5} = \frac{-6 }{-2 } =3$

We can choose either point and get the correct answer. Let's choose (3, -7) :

-7 = 3 (3) + b multiply ""

-7 =9+ b subtract from both sides

-16 = b

This means that the y = mx+b form is y = 3x -16

Report an Error

Example Question #102 : Lines

Find the equation for the line passing through the points (6,2) and (-3,-4) .

Possible Answers:

y = 2x+2

$y =- \frac{2}{3}x + 6$

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

y = 2x - 2

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

Correct answer:

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

Explanation:

To determine the equation, first find the slope:

$\frac{\Delta y}{\Delta x} = \frac{2--4}{6--3} = \frac{6}{9 } =\frac{2}{3}$

We can choose either point and get the correct answer. Let's choose (6, 2) :

$2 = \frac{2}{3} (6) + b$ multiply ""

2 = 4 + b subtract from both sides

-2 = b

This means that the y = mx+b form is $y = \frac{2}{3}x-2$

Report an Error

Example Question #1391 : Intermediate Geometry

Find the equation for the line passing through the points (5, 7) and (2, 3 ) .

Possible Answers:

$y = \frac{4}{7 } x + 1$

$y = \frac{7}{4} x + \frac{1}{2 }$

$y = \frac{3}{4} x + \frac{3}{2}$

$y = \frac{10}{3} x - \frac{11}{3}$

$y = \frac{4}{3} x + \frac{1}{3 }$

Correct answer:

$y = \frac{4}{3} x + \frac{1}{3 }$

Explanation:

First, determine the slope of the line using the slope formula:

$\frac{ \Delta y }{ \Delta x } = \frac{ y_2 - y_1 }{ x _ 2 - x_1 } = \frac{7 - 3} { 5 - 2 } = \frac{4}{3}$

The equation will be in the form y = mx + b where m is the slope that we just determined, and b is the y-intercept. To determine that, we can plug in the slope for m and the coordinates of one of the original points for x and y:

$3 = \frac{4}{3} (2) + b$

$3 = \frac{8 }{3 } + b$ to subtract, it will be easier to convert 3 to a fraction, $\frac{9}{3}$

$\frac{9}{3} - \frac{8}{3} = b$

$\frac{1}{3} = b$

The equation is $y = \frac{4}{3} x + \frac{1}{3}$

Report an Error

Example Question #11 : How To Find The Equation Of A Line

Write the equation for the line passing through the points (4, 2) and (-2,1) .

Possible Answers:

y = x + 3

$y = \frac{1}{6} x + \frac{2}{3}$

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

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

$y = \frac{1}{6} x + 1 \frac{1}{3 }$

Correct answer:

$y = \frac{1}{6} x + 1 \frac{1}{3 }$

Explanation:

First, find the slope of the line:

$\frac{ \Delta y }{ \Delta x } = \frac{2 - 1 }{ 4 - - 2 } = \frac{ 1 }{ 6 }$

Now we want to find the y-intercept. We can figure this out by plugging in the slope for "m" and one of the points in for x and y in the formula y = mx+b :

$1 = \frac{1}{6} (-2 ) + b$

$1 = -\frac{1}{3} + b$

$1 \frac{1}{3} = b$

The equation is $y = \frac{ 1}{6} x + 1 \frac{1}{3}$

Report an Error

Example Question #111 : Coordinate Geometry

Find the equation of a line passing through the points (0,-5) and (5,0) .

Possible Answers:

None of these.

y=-x-5

y=-x+5

y=x+5

y=x-5

Correct answer:

y=x-5

Explanation:

To find the equation of a line passing through these points we must find a line with that same slope. Start by finding the slope between the two points and then use the point slope equation to find the equation of the line.

slope:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{0--5}{5-0}=1$

Now use the point slope equation:

$y-y_{1}=m(x-x_{1})\rightarrow y-(-5)=1(x-0)\rightarrow \mathbf{y=x-5}$

*make sure you use the SAME coordinate pair when substituting x and y into the point slope equation.

Report an Error

Example Question #112 : Lines

Find the equation of a line that goes through the points (3, 12) and (-2, 5) .

Possible Answers:

$y=-\frac{2}{5}x-\frac{11}{5}$

$y=-\frac{1}{6}x-\frac{6}{5}$

$y=\frac{7}{5}x+\frac{39}{5}$

$y=\frac{2}{3}x+\frac{4}{9}$

Correct answer:

$y=\frac{7}{5}x+\frac{39}{5}$

Explanation:

Recall that the slope-intercept form of a line:

y=mx+b ,

where $m=\text{slope}$ and $b=\text{y-intercept}$ .

First, find the slope of the line by using the following formula:

$\text{Slope of Line}=\frac{y_2-y_1}{x_2-x_1}$

$\text{Slope}=\frac{5-12}{-2-3}=\frac{7}{5}$

Next, find the y-intercept of the line by plugging in of the points into the semi-completed formula.

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

Plugging in (3, 12) yields the following:

$12=\frac{7}{5}(3)+b$

Solve for .

$b+\frac{21}{5}=12$

$b=\frac{39}{5}$

The equation of the line is then $y=\frac{7}{5}x+\frac{39}{5}$ .

Report an Error

View Tutors

Krittika
Certified Tutor

University of Dhaka, Master's/Graduate, Statistics. University of Waterloo, Master's/Graduate, Biostatistics.

View Tutors

Alex
Certified Tutor

Vanderbilt University, Bachelor of Science, Psychology. Boston University, Master of Science, Speech-Language Pathology.

View Tutors

Mudassara
Certified Tutor

CUNY College of Staten Island, Master of Arts, Business Administration and Management.

All Intermediate Geometry Resources

8 Diagnostic Tests 250 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Computer Science Tutors in Los Angeles, Chemistry Tutors in Phoenix, ISEE Tutors in Chicago, English Tutors in Denver, LSAT Tutors in Seattle, GRE Tutors in Miami, SSAT Tutors in Washington DC, Math Tutors in Boston, Statistics Tutors in Seattle, English Tutors in San Francisco-Bay Area

Popular Courses & Classes

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

Popular Test Prep

ACT Test Prep in Boston, SSAT Test Prep in Atlanta, ACT Test Prep in Los Angeles, LSAT Test Prep in Boston, GMAT Test Prep in Houston, GMAT Test Prep in Denver, MCAT Test Prep in Phoenix, LSAT Test Prep in Chicago, ACT Test Prep in Philadelphia, GRE Test Prep in Boston

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

Intermediate Geometry : Other Lines

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

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

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

Example Question #4 : How To Find The Equation Of A Line

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

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

Example Question #102 : Lines

Example Question #1391 : Intermediate Geometry

Example Question #11 : How To Find The Equation Of A Line

Example Question #111 : Coordinate Geometry

Example Question #112 : Lines

All Intermediate Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: