Call Now to Set Up Tutoring:

(888) 888-0446

SAT Math : How to find the equation of a line

Study concepts, example questions & explanations for SAT Math

Create An Account

All SAT Math Resources

16 Diagnostic Tests 660 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #12 : Slope And Line Equations

$\small \textup{Which is the equation of the line that passes through the points}$

$\small (1,2)\,\textup{and}\,(3.8)?$

Possible Answers:

$\small y=3x+2$

$\small y = x+5$

$\small y=-3x +2$

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

$\small y=3x-1$

Correct answer:

$\small y=3x-1$

Explanation:

Equation of line: $\small y = mx+b$ , $\small m$ = slope, $\small b$ = -intercept

Step 1) Find slope ( $\small m$ ): rise/run $\small \frac{8-2}{3-1}=\frac{6}{2}=3$

Step 2) Find -intercept ( $\small b$ ): $\small \frac{2-b}{1-0}=3$

$\small 2-b = 3$

$\small 2 = 3 + b$

$\small -1 =b$

$\small y=3x-1$

Report an Error

Example Question #21 : Psat Mathematics

Whast line goes through the points (1,3) and (7,5) ?

Possible Answers:

x+y=4

x-2y=6

3x-2y=9

4x+3y=7

-x+3y=8

Correct answer:

-x+3y=8

Explanation:

Let $P_{1}=(1,3)$ and $P_{2}=(7,5)$

The slope is geven by: $m = (y_{2} - y_{1}) \div (x_{2} - x_{1})$ so

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

Then we use the slope-intercept form of an equation; y=mx+b so

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

And we convert

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

to standard form.

Report an Error

Example Question #131 : Lines

What is the equation of the line that passes through the points (4,7) and (8,10)?

Possible Answers:

-3x-4y=16

3x+4y=-16

3x-4y=-16

3x+4y=16

3x-4y=16

Correct answer:

3x-4y=-16

Explanation:

In order to find the equation of the line, we will first need to find the slope between the two points through which it passes. The slope, , of a line that passes through the points (x_1,y_1) and (x_2,y_2) is given by the formula below:

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

We are given our two points, (4,7) and (8,10), allowing us to calculate the slope.

$m=\frac{10-7}{8-4}=\frac{3}{4}$

Next, we can use point slope form to find the equation of a line with this slope that passes through one of the given points. We will use (4,7).

y-y_1=m(x-x_1)

$y-7=\frac{3}{4}(x-4)$

Multiply both sides by four to eliminate the fraction, and simplify by distribution.

$4(y-7)=4(\frac{3}{4})(x-4)$

4y-28=3(x-4)

4y-28=3x-12

Subtract from both sides and add twelve to both sides.

-28=3x-4y-12

-16=3x-4y

This gives our final answer: 3x-4y=-16

Report an Error

Example Question #132 : Lines

Which line contains the following ordered pairs:

$\left ( -2,4 \right )$ and $\left ( 6,2 \right )$

Possible Answers:

$\small y=-x+14$

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

$\small y=x+14$

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

Correct answer:

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

Explanation:

First, solve for slope.

$\small m=\frac{\Delta y}{\Delta x}=\frac{2-4}{6-(-2)}=\frac{-2}{8}=-\frac{1}{4}$

Then, substitute one of the points into the equation y=mx+b.

$\small 2=(-\frac{1}{4})(6)+b$

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

$\small b=2+\frac{3}{2}=\frac{7}{2}$

This leaves us with the equation $\small y=-\frac{1}{4}+\frac{7}{2}$

Report an Error

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

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

Act_math_160_04

Possible Answers:

y=x-4

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

y=-x

y=-5x-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 #141 : Coordinate Geometry

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

Possible Answers:

y = 1/5x + 3

y = 2/3 + 5

y = –3/2 – 3

y = 2/3x –6

y = –3/2x + 6

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 #1 : How To Find The Equation Of A Line

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

Possible Answers:

2x – 3y = 5

4x – 5y = 4

3x + 5y = 2

–3x + 2y = 3

–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 #2 : How To Find The Equation Of A Line

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

Possible Answers:

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

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

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

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

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

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 #531 : Geometry

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 #1 : Coordinate Geometry

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=-8x+38

y=-8x-38

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

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

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

View SAT Mathematics Tutors

Troy
Certified Tutor

Rice University, Bachelor in Arts, Kinesiology.

View SAT Mathematics Tutors

Sarah
Certified Tutor

New York University, Bachelor of Fine Arts, Drama.

View SAT Mathematics Tutors

Joy
Certified Tutor

Boston University, Bachelor in Arts, Conservation Biology.

All SAT Math Resources

16 Diagnostic Tests 660 Practice Tests Question of the Day Flashcards Learn by Concept

SAT Math Tutors in Top Cities:

Atlanta SAT Math Tutors, Austin SAT Math Tutors, Boston SAT Math Tutors, Chicago SAT Math Tutors, Dallas Fort Worth SAT Math Tutors, Denver SAT Math Tutors, Houston SAT Math Tutors, Kansas City SAT Math Tutors, Los Angeles SAT Math Tutors, Miami SAT Math Tutors, New York City SAT Math Tutors, Philadelphia SAT Math Tutors, Phoenix SAT Math Tutors, San Diego SAT Math Tutors, San Francisco-Bay Area SAT Math Tutors, Seattle SAT Math Tutors, St. Louis SAT Math Tutors, Tucson SAT Math Tutors, Washington DC SAT Math Tutors

Popular Courses & Classes

MCAT Courses & Classes in Phoenix, LSAT Courses & Classes in Atlanta, Spanish Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in Seattle, GMAT Courses & Classes in Denver, LSAT Courses & Classes in Miami, MCAT Courses & Classes in Los Angeles, LSAT Courses & Classes in Los Angeles, Spanish Courses & Classes in Miami, ISEE Courses & Classes in Dallas Fort Worth

Popular Test Prep

SSAT Test Prep in New York City, SAT Test Prep in Los Angeles, GRE Test Prep in Chicago, MCAT Test Prep in Los Angeles, LSAT Test Prep in Washington DC, SSAT Test Prep in Philadelphia, ISEE Test Prep in Chicago, SSAT Test Prep in San Diego, GRE Test Prep in Houston, SSAT Test Prep in Los Angeles

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

SAT Math : How to find the equation of a line

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #12 : Slope And Line Equations

Example Question #21 : Psat Mathematics

Example Question #131 : Lines

Example Question #132 : Lines

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

Example Question #141 : Coordinate Geometry

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

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

Example Question #531 : Geometry

Example Question #1 : Coordinate Geometry

All SAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: