Call Now to Set Up Tutoring:

(888) 888-0446

Algebra 1 : Equations of Lines

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 #161 : Equations Of Lines

A line passes through the points (3, 9) and (5, 3), and has a y-intercept of 3. Which of the following is an equation for that line?

Possible Answers:

y = 8x-12

$\small y = 9x-6$

$\small y = -4x + 8$

y = -2x-4

$\small \small y = -{3}x + 3$

Correct answer:

$\small \small y = -{3}x + 3$

Explanation:

The equation for a line is always $\small y = mx + b$ , where $\small m = slope$ and $\small b = y-intercept$ .

Given two data points, we are able to find the slope, m, using the formula

$\small \frac{y_{1}-y_{2}}{x_{1}-x_{2}}$ .

Using the data points provided, our formula will be:

$\small \small \frac{3-9}{5-3}$ , which gives us $\small \small -\frac{6}{2} ,$ or , $\small \small m = -3$ .

Our y-intercept is given.

Thus our equation for the line containing these points and that y-intercept is $\small \small y = -{3}x + 3$ .

Report an Error

Example Question #1 : How To Find Slope Of A Line

What is the slope of the equation 4x + 3y = 7?

Possible Answers:

–7/3

–4/3

3/4

–3/4

4/3

Correct answer:

–4/3

Explanation:

We should put this equation in the form of y = mx + b, where m is the slope.

We start with 4x + 3y = 7.

Isolate the y term: 3y = 7 – 4x

Divide by 3: y = 7/3 – 4/3 * x

Rearrange terms: y = –4/3 * x + 7/3, so the slope is –4/3.

Report an Error

Example Question #1 : How To Find Slope Of A Line

Find the slope of the line through the points (6,2) and (3,4).

Possible Answers:

$\frac{3}{2}$

$\frac{2}{3}$

$-\frac{3}{2}$

$-\frac{2}{3}$

Correct answer:

$-\frac{2}{3}$

Explanation:

The equation for slope is $\frac{(y_2-y_1)}{(x_2-x_1)}$ . You plug in the coordinates from the points given you, and get $\frac{(4-2)}{(3-6)}$ , giving you $\frac{2}{-3}$ . Note that it does not matter which point you use as point 1 and point 2, as long as you are consistent.

$\frac{(y_2-y_1)}{(x_2-x_1)}$

(6,2) = (x₁,y₁)

(3,4) = (x₂,y₂)

$\frac{(4-2)}{(3-6)}=\frac{2}{-3}=-\frac{2}{3}$

Report an Error

Example Question #1 : How To Find Slope Of A Line

Given the line 4y = 2x + 1, what is the slope of this line?

Possible Answers:

–2

–1/4

1/4

1/2

Correct answer:

1/2

Explanation:

4y = 2x + 1 becomes y = 0.5x + 0.25. We can read the coefficient of x, which is the slope of the line.

4y = 2x + 1

(4y)/4 = (2x)/4 + (1)/4

y = 0.5x + 0.25

y = mx + b, where the slope is equal to m.

The coefficient is 0.5, so the slope is 1/2.

Report an Error

Example Question #1 : How To Find Slope Of A Line

What is the slope of the line containing the points (7,12) and (91,32).

Possible Answers:

$\frac{44}{49}$

$\frac{51}{30}$

$\frac{3}{32}$

$\frac{5}{21}$

Correct answer:

$\frac{5}{21}$

Explanation:

To find the slope of a line you must first assign variables to each point. It does not matter which points get which variables as long as you keep the $x_{1}$ and $y_{1}$ and $x_{2}$ and $y_{2}$ consistent when you plug them into the equation.

Then we plug in the variables to this equation where represents the slope. $m=\frac{(y_{2}-y_{1})}{(x_{2}-x_{1})}$

Then we plug in our points for $x_{1},x_{2},y_{1},and\ y_{2}$ and the example looks like $m=\frac{(32-12)}{(91-7)}$

Then we perform the necessary subtraction and division to find an answer of $m=\frac{20}{84}=\frac{5}{21}$

Report an Error

Example Question #2 : How To Find Slope Of A Line

$\textup{What is the slope of the linear equation }3y-4x=13\textup{ ?}$

Possible Answers:

$\frac{3}{4}$

$-\frac{3}{4}$

$\frac{4}{3}$

$-\frac{4}{3}$

$\frac{13}{3}$

Correct answer:

$\frac{4}{3}$

Explanation:

$\textup{To find the slope, put the equation into }y=mx+b\textup{ format.}$

3y-4x=13

3y=4x+13

$y = \frac{4}{3}x+\frac{13}{3}\;\;\;\;\;\;\textup{slope}=m = \frac{4}{3}$

Report an Error

Example Question #2 : How To Find Slope Of A Line

Which of the following is an example of an equation written in slope-intercept form?

Possible Answers:

y=-x+4

y+x=4

y+x-4=0

-y=x-4

Correct answer:

y=-x+4

Explanation:

Slope intercept form is y=mx+b , where is the slope and is the y-intercept.

y=-x+4 is the correct answer. The line has a slope of and a y-intercept equal to .

Report an Error

Example Question #1 : How To Find Slope Of A Line

If (1,2) and (4,6) are on the same line, what is the slope of the line?

Possible Answers:

$\frac{4}{3}$

$\frac{1}{2}$

$\frac{3}{4}$

Correct answer:

$\frac{4}{3}$

Explanation:

$m=slope=\frac{\Delta y}{\Delta x}=\frac{\left ( y_{2}-y_{1}\right )}{\left ( x_{2}-x_{1}\right )}=$

$\frac{\left ( 6-2\right )}{\left ( 4-1\right )}=\frac{4}{3}$

Report an Error

Example Question #1 : How To Find Slope Of A Line

The equation of a line is:

5x+25y=14

What is the slope of the line?

Possible Answers:

$\frac{14}{25}$

$-\frac{1}{5}$

$-\frac{14}{25}$

$\frac{1}{5}$

Correct answer:

$-\frac{1}{5}$

Explanation:

Solve the equation for y=mx+b

where is the slope of the line:

5x+25y=14

25y=-5x+14

$y=-\left ( \frac{5}{25} \right )x+\frac{14}{25}=-\left ( \frac{1}{5} \right )x+\frac{14}{25}$

$Slope=-\frac{1}{5}$

Report an Error

Example Question #1 : How To Find Slope Of A Line

A line passes through the points (-1,4) and (4,-9) . What is its slope?

Possible Answers:

$\frac{5}{13}$

$\frac{13}{5}$

$-\frac{13}{5}$

- $-\frac{5}{13}$

Correct answer:

$-\frac{13}{5}$

Explanation:

The slope is the rise over the run. The line drops in -coordinates by 13 while gaining 5 in the -coordinates.

Report an Error

View Algebra Tutors

Aylar
Certified Tutor

Mercer University, Bachelor of Science, Mechanical Engineering.

View Algebra Tutors

Liban
Certified Tutor

Emory University, Bachelor of Science, Mathematics/Economics.

View Algebra Tutors

Akira
Certified Tutor

Prairie State College, Associate, General Education. Prairie State College, Associate, Industrial Electrician .

All Algebra 1 Resources

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

Popular Subjects

Algebra Tutors in New York City, Biology Tutors in Boston, Reading Tutors in Phoenix, Reading Tutors in Philadelphia, Chemistry Tutors in Philadelphia, Reading Tutors in Dallas Fort Worth, SAT Tutors in Miami, GRE Tutors in Miami, English Tutors in New York City, MCAT Tutors in Chicago

Popular Courses & Classes

ACT Courses & Classes in Los Angeles, Spanish Courses & Classes in San Diego, SSAT Courses & Classes in Philadelphia, ACT Courses & Classes in Boston, MCAT Courses & Classes in Philadelphia, SAT Courses & Classes in Miami, GMAT Courses & Classes in Seattle, SAT Courses & Classes in Houston, LSAT Courses & Classes in Seattle, MCAT Courses & Classes in Denver

Popular Test Prep

LSAT Test Prep in Phoenix, ISEE Test Prep in Boston, SSAT Test Prep in Philadelphia, MCAT Test Prep in Washington DC, SSAT Test Prep in San Francisco-Bay Area, MCAT Test Prep in Denver, GRE Test Prep in Boston, MCAT Test Prep in Los Angeles, SAT Test Prep in Philadelphia, LSAT Test Prep in Miami

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 : Equations of Lines

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #161 : Equations Of Lines

Example Question #1 : How To Find Slope Of A Line

Example Question #1 : How To Find Slope Of A Line

Example Question #1 : How To Find Slope Of A Line

Example Question #1 : How To Find Slope Of A Line

Example Question #2 : How To Find Slope Of A Line

Example Question #2 : How To Find Slope Of A Line

Example Question #1 : How To Find Slope Of A Line

Example Question #1 : How To Find Slope Of A Line

Example Question #1 : How To Find Slope Of A Line

All Algebra 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: