Call Now to Set Up Tutoring:

(888) 888-0446

SAT Math : How to graph 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 #1 : How To Graph A Line

A line graphed on the coordinate plane below. Graph_of_y_-2x_4

Give the equation of the line in slope intercept form.

Possible Answers:

$\dpi{100} \small y=2x+4$

$\dpi{100} \small y=2x-4$

$\dpi{100} \small y=-2x+4$

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

$\dpi{100} \small y=-2x-4$

Correct answer:

$\dpi{100} \small y=-2x+4$

Explanation:

The slope of the line is $\dpi{100} \small -2$ and the y-intercept is $\dpi{100} \small 4$ .

The equation of the line is $\dpi{100} \small y=-2x+4$ .

Report an Error

Example Question #13 : Graphing

Graph_of_y_-x_3

Give the equation of the curve.

Possible Answers:

$\dpi{100} \small y=x^{3}$

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

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

None of the other answers

$\dpi{100} \small y=x^{4}$

Correct answer:

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

Explanation:

Graph_of_x_3 This is the parent graph of $\dpi{100} \small x^{3}$ . Since the graph in question is negative, then we flip the quadrants in which it will approach infinity. So the graph of $\dpi{100} \small y=-x^{3}$ will start in quadrant 2 and end in 4.

Report an Error

Example Question #16 : Graphing

Give the area of the triangle on the coordinate plane that is bounded by the lines of the equations y = -2 , y = x and y = 4x- 7 .

Possible Answers:

$7\frac{7}{12}$

$3\frac{19}{24}$

$1 \frac{11}{24}$

$7 \frac{1}{24}$

$2 \frac{11}{12}$

Correct answer:

$7 \frac{1}{24}$

Explanation:

It is necessary to find the coordinates of the vertices of the triangle, each of which is the intersection of two of the three lines.

The intersection of the lines of the equations y = -2 and y = x can be found by noting that, by substituting for in the latter equation, -2 = x , making the point of intersection (-2,-2) .

The intersection of the lines of the equations y = -2 and y = 4x- 7 can be found by substituting for in the latter equation and solving for :

4x- 7 = -2

4x- 7 + 7 = -2 + 7

4x = 5

$\frac{4x}{4} = \frac{5}{4}$

$x = 1 \frac{1}{4}$

This point of intersection is $\left ( 1 \frac{1}{4}, -2 \right )$ .

The intersection of the lines of the equations y = x and y = 4x- 7 can be found by substituting for in the latter equation and solving for :

4x- 7 = x

4x- 7 - x + 7 = x - x + 7

3x = 7

$\frac{3x }{3}= \frac{7}{3}$

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

Since y = x , $y = 2\frac{1}{3}$ , and this point of intersection is $\left ( 2\frac{1}{3}, 2\frac{1}{3} \right )$ .

The lines in question are graphed below, and the triangle they bound is shaded:

Triangle z

We can take the horizontal side as the base of the triangle; its length is the difference of the -coordinates:

$b = 1\frac{1}{4} - (-2 ) = 3 \frac{1}{4}$

The height is the vertical distance from this side to the opposite side, which is the difference of the -coordinates:

$h = 2 \frac{1}{3} - (-2) = 4 \frac{1}{3}$

The area is half their product:

$A = \frac{1}{2} bh = \frac{1}{2} \cdot 3 \frac{1}{4} \cdot 4 \frac{1}{3} =7 \frac{1}{24}$

Report an Error

Example Question #664 : Sat Mathematics

Billy set up a ramp for his toy cars. He did this by taking a wooden plank and putting one end on top of a brick that was 3 inches high. He then put the other end on top of a box that was 9 inches high. The bricks were 18 inches apart. What is the slope of the plank?

Possible Answers:

$\frac{1}{3}$

$\frac{3}{18}$

$\frac{5}{9}$

$\frac{1}{18}$

Correct answer:

$\frac{1}{3}$

Explanation:

The value of the slope (m) is rise over run, and can be calculated with the formula below:

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

The coordinates of the first end of the plank would be (0,3), given that this is the starting point of the plank (so x would be 0), and y would be 3 since the brick is 3 inches tall.

The coordinates of the second end of the plank would be (18,9) since the plank is 18 inches long (so x would be 18) and y would be 9 since the box was 9 inches tall at the other end.

From this information we know that we can assign the following coordinates for the equation:

$\left(x_{1},y_{1}\right) = (0,3)$ and $(x_{2}, y_{2})= (18,9)$

Below is the solution we would get from plugging this information into the equation for slope:

$m = \frac{9-3}{18-0}}$

This reduces to $\frac{6}{18} =\frac{1}{3}$

Report an Error

Example Question #2 : How To Find A Line On A Coordinate Plane

What is the slope of the line depicted by the graph?

Screen shot 2016 02 10 at 9.35.05 am

Possible Answers:

$\frac{5}{8}$

$\frac{8}{5}$

Correct answer:

$\frac{5}{8}$

Explanation:

Looking at the graph, it is seen that the line passes through the points (-8,-5) and (8,5).

Screen shot 2016 02 10 at 9.35.05 am

The slope of a line through the points (8, 5) and (-8,- 5) can be found by setting

$x_{1} = -8,y_{1} = -5, x_{2} = 8, y_{2} = 5$ :

in the slope formula:

$m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}} = \frac{5-(-5)}{8 - (-8)} = \frac{5+5}{8 + 8} = \frac{10}{16} = \frac{5}{8}$

Report an Error

Example Question #2 : How To Graph A Line

Screen shot 2016 01 12 at 2.32.17 pm

What is the -intercept of the function that is depicted in the graph above?

Possible Answers:

$\text{y-intercept}=4$

$\text{y-intercept}=-3$

$\text{y-intercept}=2$

$\text{y-intercept}=3$

$\text{y-intercept}=1$

Correct answer:

$\text{y-intercept}=3$

Explanation:

This question tests one's ability to recognize algebraic characteristics of a graph. This particular question examines a linear function.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the general algebraic function for the given graph.

Since the graph is that of a straight line, the general algebraic form of the function is,

y=mx+b

where

$\\m=\textup{slope} \\b=\textup{y-intercept}$

Step 2: Identify where the graph crosses the -axis.

Screen shot 2016 01 12 at 2.32.17 pm

Therefore the general form of the function looks like,

y=mx+3

Step 3: Answer the question.

The -intercept is three.

Report an Error

Example Question #5 : How To Graph A Line

The equation 3x + 2y = 6 represents a line. This line does NOT pass through which of the four quadrants?

Possible Answers:

III

Cannot be determined

Correct answer:

III

Explanation:

Plug in for to find a point on the line:

3(0) + 2y = 6

y = 3

Thus, (0,3) is a point on the line.

Plug in for to find a second point on the line:

3x + 2(0) = 6

x = 2

(2,0) is another point on the line.

Now we know that the line passes through the points (2,0) and (0,3) .

A quick sketch of the two points reveals that the line passes through all but the third quadrant.

Report an Error

View SAT Mathematics Tutors

Miriam
Certified Tutor

Washington University in St Louis, Bachelor in Arts, Biology, General.

View SAT Mathematics Tutors

Liban
Certified Tutor

Emory University, Bachelor of Science, Mathematics/Economics.

View SAT Mathematics Tutors

Irina
Certified Tutor

New York University, Bachelors, Biochemistry.

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

GMAT Courses & Classes in Denver, ACT Courses & Classes in Boston, Spanish Courses & Classes in Phoenix, Spanish Courses & Classes in Houston, LSAT Courses & Classes in Atlanta, Spanish Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Houston, ACT Courses & Classes in Houston, MCAT Courses & Classes in San Francisco-Bay Area

Popular Test Prep

GRE Test Prep in San Francisco-Bay Area, ISEE Test Prep in Boston, SAT Test Prep in Denver, ACT Test Prep in Houston, GMAT Test Prep in New York City, SAT Test Prep in Houston, SAT Test Prep in Boston, GRE Test Prep in Atlanta, MCAT Test Prep in Houston, GRE 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

SAT Math : How to graph a line

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #1 : How To Graph A Line

Example Question #13 : Graphing

Example Question #16 : Graphing

Example Question #664 : Sat Mathematics

Example Question #2 : How To Find A Line On A Coordinate Plane

Example Question #2 : How To Graph A Line

Example Question #5 : How To Graph A Line

All SAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: