Call Now to Set Up Tutoring:

(888) 888-0446

Algebra 1 : How to find the equation of a line

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 #11 : Slope And Line Equations

Which of these lines has a slope of and a -intercept of ?

Possible Answers:

y=-6x+4

None of the other answers

y=4x-6

y=4x+6

y=2x-3

Correct answer:

y=4x-6

Explanation:

When a line is in the y=mx+b form, the is its slope and the is its -intercept. Thus, the only line with a slope of and a -intercept of is

y=4x-6 .

Report an Error

Example Question #12 : Slope And Line Equations

What is the equation of a line with a slope of 3 that runs through the point (4,9)?

Possible Answers:

y=-3x-3

None of the other answers

y=3x-3

y=-3x+3

y=3x+3

Correct answer:

y=3x-3

Explanation:

You can find the equation by plugging in all of the information to the y=mx+b formula.

The slope (or ) is 3. So, the equation is now y=3x+b .

You are also given a point on the line: (4,9), which you can plug into the equation:

9=3(4)+b

Solve for to get b=-3 .

Now that you have the and , you can determine that the equation of the line is y=3x-3 .

Report an Error

Example Question #13 : Slope And Line Equations

What is the equation of the line passing through the points (1,2) and (3,1) ?

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

First find the slope of the 2 points:

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

Then use the slope and one of the points to find the y-intercept:

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

$\frac{4}{2}+\frac{1}{2}=-\frac{1}{2}+\frac{1}{2}+b$

$\frac{5}{2}=b$

So the final equation is $y=-\frac{1}{2}x+\frac{5}{2}$

Report an Error

Example Question #14 : Slope And Line Equations

What is the slope and y-intercept of 2y-4x=12 ?

Possible Answers:

None of the other answers

Slope: ; y-intercept:

Correct answer:

Slope: ; y-intercept:

Explanation:

The easiest way to determine the slope and y-intercept of a line is by rearranging its equation to the y=mx+b form. In this form, the slope is the and the y-intercept is the .

Rearranging 2y-4x=12

gives you

y=2x+6

which has an of 2 and a of 6.

Report an Error

Example Question #15 : Slope And Line Equations

Find the equation of the line, in y=mx+b form, that contains the points (1,6) , (11,12) , and (-9,0) .

Possible Answers:

$y = \frac{5}{3}x + \frac{13}{3}$

$y=\frac{3}{5}x +\frac{27}{5}$

$y = \frac{3}{5}x - 7$

y = 10x - 4

y = 3x +5

Correct answer:

$y=\frac{3}{5}x +\frac{27}{5}$

Explanation:

When finding the equation of a line given two or more points, the first step is to find the slope of that line. We can use the slope equation, $\frac{y_{2}-y_{_{1}}}{x_{2}-x_{1}}$ . Any combination of the three points can be used, but let's consider the first two points, (1,6) and (11,12) .

$\frac{12-6}{11-1} = \frac{3}{5}$

So $\frac{3}{5}$ is our slope.

Now, we have the half-finished equation

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

and we can complete it by plugging in the and values of any point. Let's use (1,6) .

Solving

$6 = \frac{3}{5}(1)+b$

for gives us

$b = 6 - \frac{3}{5}$

$b = 5\frac{2}{5} = \frac{27}{5}$

We now have our completed equation:

$y = \frac{3}{5}x + \frac{27}{5}$

Report an Error

Example Question #16 : Slope And Line Equations

We have two points: (-3,-1) and (4,9) .

If these two points are connected by a straight line, find the equation describing this straight line.

Possible Answers:

None of these

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

$y=\frac{10}{3}x+\frac{3}{7}$

$y=\frac{10}{7}x+\frac{23}{7}$

$y=-\frac{10}{3}x+\frac{3}{7}$

Correct answer:

$y=\frac{10}{7}x+\frac{23}{7}$

Explanation:

We need to find the equation of the line in slope-intercept form.

y=mx+b

In this formula, is equal to the slope and is equal to the y-intercept.

To find this equation, first, we need to find the slope by using the formula for the slope between two point.

$m=\frac{y_2-y_1}{x_2-x_1}$

In the formula, the points are and . In our case, the points are (-3,-1) and (4,9) . Using our values allows us to solve for the slope.

$m=\frac{9-(-1)}{4-(-3)}=\frac{10}{7}$

We can replace the variable with our new slope.

$y=\frac{10}{7}x+b$

Next, we need to find the y-intercept. To find this intercept, we can pick one of our given points and use it in the formula.

(-3,-1)

$-1=\frac{10}{7}(-3)+b$

Solve for .

$-1=\frac{-30}{7}+b$

$b=-1+\frac{30}{7}$

$b=\frac{23}{7}$

Now, the final equation connecting the two points can be written using the new value for the y-intercept.

$y=\frac{10}{7}x+\frac{23}{7}$

Report an Error

Example Question #17 : Slope And Line Equations

Which of these lines has a slope of and a y-intercept of ?

Possible Answers:

y=-4x+3

y=3x-4

None of the other answers

y=-3x+4

y=4x-3

Correct answer:

y=-3x+4

Explanation:

Since all of the answers are in the y=mx+b form, the slope of each line is indicated by its and its y-intercept is indicated by its . Thus, a line with a slope of and a y-intercept of must have an equation of y=-3x+4 .

Report an Error

Example Question #18 : Slope And Line Equations

Find the domain of:

$\sqrt{2x-5}$

Possible Answers:

$\left \{ x|x= \frac{5}{2} \right \}$

$\left \{ x|x\neq \frac{5}{2} \right \}$

$\left \{ x|x\geq \frac{5}{2} \right \}$

$\left \{ x|x\leq \frac{5}{2} \right \}$

$\left \{ x|-\infty < x< \infty \right \}$

Correct answer:

$\left \{ x|x\geq \frac{5}{2} \right \}$

Explanation:

The expression under the radical must be $\geq 0$ . Hence

$\sqrt{2x-5} \geq 0$

Solving for , we get

$x\geq \frac{5}{2}$

Report an Error

Example Question #19 : Slope And Line Equations

Give, in slope-intercept form, the equation of a line through the points (-2, 5) and (-3, 8) .

Possible Answers:

y = -3x -7

y = -3x +5

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

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

y = -3x -1

Correct answer:

y = -3x -1

Explanation:

First, use the slope formula to find the slope, setting $x_{1} = -2, y_{1} = 5,x_{2} = -3, y_{2} = 8$ .

$m = \frac{y _{2} - y_{1}}{x _{2} - x_{1}} = \frac{8 -5 }{-3-(-2)} = \frac{3 }{-1} = -3$

We can write the equation in slope-intercept form as

y = mx + b .

Replace m = -3 :

y = -3x + b

We can find by substituting for x,y using either point - we will choose (-2, 5) :

5= -3 (-2) + b

5= 6 + b

5-6 = 6 -6 + b

b = -1

The equation is y = -3x -1 .

Report an Error

Example Question #20 : Slope And Line Equations

Give, in slope-intercept form, the equation of a line through the points $\left (3.5, 5.5 \right )$ and (5.5, -2.5) .

Possible Answers:

y = -4x + 2.5

y = -4x + 3.5

y = -4x + 19.5

y = -0.25x + 5.5

y = -0.25x + 13.5

Correct answer:

y = -4x + 19.5

Explanation:

First, use the slope formula to find the slope, setting $x_{1} = 3.5, y_{1} = 5.5,x_{2} = 5.5, y_{2} = -2.5$ .

$m = \frac{y _{2} - y_{1}}{x _{2} - x_{1}} = \frac{-2.5 -5.5}{5.5-3.5} = \frac{-8 }{2} = -4$

We can write the equation in slope-intercept form as

y = mx + b .

Replace m = -4 :

y = -4x + b

We can find by substituting for x,y using either point - we will choose (3.5, 5.5) :

5.5= -4 (3.5) + b

5.5= -14 +b

5.5+14 = -14 +14+b

b = 19.5

The equation is y = -4x + 19.5 .

Report an Error

View Algebra Tutors

Liban
Certified Tutor

Emory University, Bachelor of Science, Mathematics/Economics.

View Algebra Tutors

Denys
Certified Tutor

Lviv National University Ukraine, Bachelors, Biology/Biophysics. University of Szeged Hungary, PHD, Computational Biophysics.

View Algebra Tutors

Keith
Certified Tutor

Xavier University, Bachelor in Business Administration, Accounting. Ohio University-Main Campus, Masters in Education, Mathem...

All Algebra 1 Resources

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

Popular Subjects

ISEE Tutors in New York City, Math Tutors in Dallas Fort Worth, Math Tutors in San Francisco-Bay Area, SAT Tutors in Denver, GRE Tutors in Phoenix, LSAT Tutors in Miami, Chemistry Tutors in Denver, GMAT Tutors in San Diego, English Tutors in Houston, Biology Tutors in New York City

Popular Courses & Classes

MCAT Courses & Classes in Houston, MCAT Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in Houston, SAT Courses & Classes in New York City, LSAT Courses & Classes in Atlanta, Spanish Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in Boston, MCAT Courses & Classes in Chicago, ACT Courses & Classes in New York City, GRE Courses & Classes in Atlanta

Popular Test Prep

ISEE Test Prep in Seattle, SAT Test Prep in Dallas Fort Worth, ISEE Test Prep in San Diego, SSAT Test Prep in New York City, MCAT Test Prep in Washington DC, SSAT Test Prep in Houston, ISEE Test Prep in Washington DC, ISEE Test Prep in Los Angeles, LSAT Test Prep in Los Angeles, MCAT Test Prep in New York City

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 : How to find the equation of a line

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #11 : Slope And Line Equations

Example Question #12 : Slope And Line Equations

Example Question #13 : Slope And Line Equations

Example Question #14 : Slope And Line Equations

Example Question #15 : Slope And Line Equations

Example Question #16 : Slope And Line Equations

Example Question #17 : Slope And Line Equations

Example Question #18 : Slope And Line Equations

Example Question #19 : Slope And Line Equations

Example Question #20 : Slope And Line Equations

All Algebra 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: