We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Intermediate Geometry : How to find the equation of a line

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

← Previous 1 2 3 4 Next →

Example Question #31 : Other Lines

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

Possible Answers:

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

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

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

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

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

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 #32 : Other Lines

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

Possible Answers:

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

y = x + 3

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

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

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

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 #33 : Other Lines

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

Possible Answers:

y=x-5

None of these.

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 #34 : Other Lines

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

Possible Answers:

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

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

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

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

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

Example Question #41 : Other Lines

Find the equation of a line that goes through the points (-10, 7) and (12, 8)} .

Possible Answers:

y=22x+5

$y=\frac{5}{18}x+\frac{1}{9}$

$y=-\frac{18}{19}x-\frac{6}{19}$

$y=\frac{1}{22}x+\frac{82}{11}$

Correct answer:

$y=\frac{1}{22}x+\frac{82}{11}$

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:

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

$\text{Slope}=\frac{8-7}{12-(-10)}=\frac{1}{22}$

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

$y=\frac{1}{22}x+b$

Plugging in (12, 8) yields the following:

$8=\frac{1}{22}(12)+b$

Solve for .

$b+\frac{6}{11}=8$

$b=\frac{82}{11}$

The equation of the line is then $y=\frac{1}{22}x+\frac{82}{11}$ .

Report an Error

Example Question #42 : Other Lines

Find the equation of a line that goes through the points (16, 10) and (15, 2) .

Possible Answers:

$y=-\frac{1}{4}x-111$

y=8x-118

y=4x+108

$y=\frac{1}{8}x+112$

Correct answer:

y=8x-118

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:

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

$\text{Slope}=\frac{10-2}{16-15}=8$

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

y=8x+b

Plugging in (16, 10) yields the following:

10=8(16)+b

Solve for .

b+128=10

b=-118

The equation of the line is then y=8x-118 .

Report an Error

Example Question #43 : Other Lines

Find the equation of a line that goes through the points (-3, -5) and (-4, 8) .

Possible Answers:

y=-12x+32

y=-13x-44

$y=-\frac{2}{13}x-\frac{16}{13}$

y=-17x-29

Correct answer:

y=-13x-44

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:

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

$\text{Slope}=\frac{8-(-5)}{-4-(-3)}=-13$

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

y=-13x+b

Plugging in (-3, -5) yields the following:

-5=-13(-3)+b

Solve for .

b+39=-5

b=-44

The equation of the line is then y=-13x-44 .

Report an Error

Example Question #44 : Other Lines

Find the equation of the line that goes through the points (12, 0) and (0, 16) .

Possible Answers:

$y=-\frac{3}{4}x+12$

$y=-\frac{4}{3}x+16$

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

y=4x+16

Correct answer:

$y=-\frac{4}{3}x+16$

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:

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

$\text{Slope}=\frac{0-16}{12-0}=-\frac{4}{3}$

The y-intercept is since that is given as one of the points on the line.

The line must have the equation $y=-\frac{4}{3}x+16$ .

Report an Error

Example Question #45 : Other Lines

Find the equation of the line that goes through the points (20, 18) and (-40, -36) .

Possible Answers:

y=-8x+12

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

$y=-\frac{9}{10}x-1$

$y=\frac{10}{9}x+4$

Correct answer:

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

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:

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

$\text{Slope}=\frac{18-(-36)}{20-(-40)}=\frac{9}{10}$

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

$y=\frac{9}{10}x+b$

Plugging in (20, 18) yields the following:

$18=\frac{9}{10}(20)+b$

Solve for .

b+18=18

b=0

The equation of the line is then $y=\frac{9}{10}x$ .

Report an Error

Example Question #46 : Other Lines

Find the equation of the line that goes through the points (5, -10) and (15, 20) .

Possible Answers:

y=3x-25

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

$y=\frac{1}{3}x-10$

$y=\frac{3}{2}x+5$

Correct answer:

y=3x-25

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:

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

$\text{Slope}=\frac{20-(-10)}{15-5}=3$

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

y=3x+b

Plugging in (5, -10) yields the following:

-10=3(5)+b

Solve for .

b+15=-10

b=-25

The equation of the line is then y=3x-25 .

Report an Error

← Previous 1 2 3 4 Next →

View Tutors

Bill
Certified Tutor

SUNY Empire State College, Bachelors, General Sciences, Theater.

View Tutors

Amit Kumar
Certified Tutor

sanjay gandhi postgraduate medical science , Doctorate (PhD), Genetics molecular biology .

View Tutors

Andrew
Certified Tutor

Louisiana State University Eunice, Bachelor of Science, Computer Software Engineering.

All Intermediate Geometry Resources

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

Popular Subjects

SSAT Tutors in Denver, GMAT Tutors in Chicago, Computer Science Tutors in Philadelphia, SAT Tutors in Philadelphia, MCAT Tutors in San Francisco-Bay Area, Biology Tutors in Dallas Fort Worth, Reading Tutors in Dallas Fort Worth, Chemistry Tutors in Houston, Algebra Tutors in Philadelphia, GRE Tutors in Phoenix

Popular Courses & Classes

GMAT Courses & Classes in Denver, GRE Courses & Classes in Los Angeles, SAT Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in Los Angeles, Spanish Courses & Classes in Seattle, ACT Courses & Classes in Washington DC, SAT Courses & Classes in Washington DC, Spanish Courses & Classes in Miami, GMAT Courses & Classes in Philadelphia, SSAT Courses & Classes in Washington DC

Popular Test Prep

LSAT Test Prep in Boston, GMAT Test Prep in New York City, ACT Test Prep in Chicago, MCAT Test Prep in New York City, SAT Test Prep in San Francisco-Bay Area, ISEE Test Prep in Boston, ACT Test Prep in San Diego, ACT Test Prep in Houston, GRE Test Prep in Houston, MCAT 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)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Intermediate Geometry : How to find the equation of a line

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #31 : Other Lines

Example Question #32 : Other Lines

Example Question #33 : Other Lines

Example Question #34 : Other Lines

Example Question #41 : Other Lines

Example Question #42 : Other Lines

Example Question #43 : Other Lines

Example Question #44 : Other Lines

Example Question #45 : Other Lines

Example Question #46 : Other Lines

All Intermediate Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: