Call Now to Set Up Tutoring:

(888) 888-0446

SAT Math : How to find out if a point is on a line with an equation

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

← Previous 1 2 Next →

Example Question #100 : Coordinate Geometry

At what point do these two lines intersect?

y=2x+3

y=x+1

Possible Answers:

(2, -1)

None of the above

(-2,-1)

(-2, 1)

(2, 1)

Correct answer:

(-2,-1)

Explanation:

If two lines intersect, that means that at one point, the and values are the same. Therefore, we can use substitution to solve this problem.

Let's substitute y=2x+3 in for in the other equation. Then, solve for :

2x+3 = x+1

x=-2

Now, we can substitute this into either equation and solve for :

y=x+1

y=-2+1 = -1

With these two values, the point of intersection is (-2, -1)

Report an Error

Example Question #101 : Coordinate Geometry

At what point do these two lines intersect?

2x-3y=1

3x+2y=2

Possible Answers:

$(\frac{8}{15}, \frac{3}{15})$

(2, 1)

(1, 2)

None of the given answers

$(-\frac{8}{15}, \frac{3}{15})$

Correct answer:

$(\frac{8}{15}, \frac{3}{15})$

Explanation:

If two lines intersect, that means that their and values are the same at one point. Therefore, we can use substitution to solve this problem.

First, let's write these two formulas in slope-intercept form. First:

2x-3y=1

-3y=-2x+1

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

Then, for the second line:

2y=-3x+2

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

Now, we can substitute $y=\frac{2}{3}x - \frac{1}{3}$ in for in our second equation and solve for , like so:

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

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

$\frac{4}{6}x +\frac{9}{6}x = \frac{4}{3}$

$\frac{15}{6}x = \frac{4}{3}$

$x = \frac{24}{45} = \frac{8}{15}$

Now, we can substitute this value into either equation to solve for .

2x - 3y = 1

$2(\frac{8}{15}) - 3y =1$

$\frac{16}{15} - 3y =1$

$-3y = 1-\frac{18}{15}$

$y = -3(\frac{15}{15} - \frac{16}{15}) = -3(-\frac{1}{15}) = \frac{3}{15}$

Therefore, our point of intersection is $(\frac{8}{15}, \frac{3}{15})$

Report an Error

Example Question #102 : Coordinate Geometry

Trans

Lines P and Q are parallel. Find the value of .

Possible Answers:

$x=-5+ \sqrt{ 205}$

$x=-5- \sqrt{ 205}$

$x= \sqrt{ 205}$

$x=-5\pm \sqrt{ 205}$

$x=\pm \sqrt{ 205}$

Correct answer:

$x=-5\pm \sqrt{ 205}$

Explanation:

Since these are complementary angles, we can set up the following equation.

x^2+4+10x-4=180

x^2+10x=180

x^2+10x-180=0

Now we will use the quadratic formula to solve for .

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\frac{-10\pm \sqrt{10^2-4(1)(-180)}}{2(1)}$

$x=\frac{-10\pm \sqrt{100+720}}{2}$

$x=\frac{-10\pm \sqrt{820}}{2}$

$x=\frac{-10\pm \sqrt{4\cdot 205}}{2}$

$x=\frac{-10\pm 2\sqrt{ 205}}{2}$

$x=-5\pm \sqrt{ 205}$

Report an Error

Example Question #251 : New Sat

$\begin{tabular}{||c c||} \hline Time & Distance \\ [0.5ex] \hline\hline 0&10 \\ 1&4 \\ 2&3 \\ 2.5 & 1 \\ 3&3\\ 4&4 \\ 5&10\\ \hline \hline \end{tabular}$

The table and graph describe two different particle's travel over time. Which particle has a lower minimum?

Possible Answers:

$\text{Table}$

$\text{More information is needed}$

$\text{The table and graph are equal}$

$\text{Graph}$

Correct answer:

$\text{Graph}$

Explanation:

This question is testing one's ability to compare the properties of functions when they are illustrated in different forms. This question specifically is asking for the examination and interpretation of two quadratic functions for which one is illustrated in a table format and the other is illustrated graphically.

Step 1: Identify the minimum of the table.

Using the table find the time value where the lowest distance exists.

$\begin{tabular}{||c c||} \hline Time & Distance \\ [0.5ex] \hline\hline 0&10 \\ 1&4 \\ 2&3 \\ {\color{Red} 2.5} & {\color{Red} 1} \\ 3&3\\ 4&4 \\ 5&10\\ \hline \hline \end{tabular}$

Recall that the time represents the values while the distance represents the values. Therefore the ordered pair for the minimum can be written as (2.5,1) .

Step 2: Identify the minimum of the graph

Recall that the minimum of a cubic function is known as a local minimum. This occurs at the valley where the vertex lies.

For this particular graph the vertex is at (1,-3) .

Step 3: Compare the minimums from step 1 and step 2.

Compare the value coordinate from both minimums.

$-3<1\Rightarrow \textup{Graph}< \textup{Table}$

Therefore, the graph has the lowest minimum.

Report an Error

Example Question #104 : Coordinate Geometry

Axes

Figure NOT drawn to scale.

On the coordinate axes shown above, the shaded triangle has the following area:

Evaluate .

Possible Answers:

$X = 3 \frac{1}{4}$

X = 3

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

$X = 3 \frac{3}{4}$

X = 4

Correct answer:

$X = 3 \frac{3}{4}$

Explanation:

The lengths of the horizontal and vertical legs of the triangle correspond to the -coordinate of the -intercept and the -coordinate of the -intercept. The area of a right triangle is half the product of the lengths of its legs and . The length of the vertical leg is b = 16 , so, setting b = 16 and A = 48 , and solving for :

$\frac{1}{2} ab = A$

$\frac{1}{2} \cdot a \cdot 16 = 48$

8a = 48

$\frac{8a }{8}= \frac{48}{8}$

a= 6

Therefore, the -intercept of the line containing the hypotenuse is (6,0 ) . The slope of the line given the coordinates of its intercepts is

$m = - \frac{b}{a}$ .

substituting:

$m = - \frac{16}{6} = -\frac{8}{3}$ .

Substituting for and in the slope-intercept form of the equation of a line,

y = mx+ b ,

the line has equation

$y = -\frac{8}{3} x+16$ .

Substituting for and 6 for and solving for , we find the -coordinate

of the point on the line with -coordinate 6:

$6 = -\frac{8}{3} X+16$

$6 + \frac{8}{3} X - 6 = -\frac{8}{3} X+16 + \frac{8}{3} X - 6$

$\frac{8}{3} X = 10$

$\frac{3} {8}\cdot \frac{8}{3} X = \frac{3} {8}\cdot 10$

$X = \frac{15} {4} = 3 \frac{3}{4}$

Report an Error

← Previous 1 2 Next →

View SAT Mathematics Tutors

Bill
Certified Tutor

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

View SAT Mathematics Tutors

Alexandra
Certified Tutor

University of Pittsburgh-Pittsburgh Campus, Bachelor in Arts, Psychology.

View SAT Mathematics Tutors

Zachary
Certified Tutor

Yale University, Bachelor of Science, Biology, General.

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

SSAT Courses & Classes in Atlanta, ISEE Courses & Classes in San Diego, ISEE Courses & Classes in Philadelphia, GMAT Courses & Classes in Los Angeles, GRE Courses & Classes in Boston, ACT Courses & Classes in Boston, ACT Courses & Classes in Philadelphia, GRE Courses & Classes in Washington DC, MCAT Courses & Classes in Houston, LSAT Courses & Classes in New York City

Popular Test Prep

SAT Test Prep in Denver, ISEE Test Prep in Philadelphia, ACT Test Prep in Boston, MCAT Test Prep in Seattle, ISEE Test Prep in San Francisco-Bay Area, LSAT Test Prep in Dallas Fort Worth, GMAT Test Prep in Los Angeles, ACT Test Prep in Denver, MCAT Test Prep in Chicago, MCAT Test Prep in San Francisco-Bay Area

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 out if a point is on a line with an equation

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #100 : Coordinate Geometry

Example Question #101 : Coordinate Geometry

Example Question #102 : Coordinate Geometry

Example Question #251 : New Sat

Example Question #104 : Coordinate Geometry

All SAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: