<< Chapter < Page Chapter >> Page >

3 x + 8 y = 9

The x- intercept is ( 3 , 0 ) and the y -intercept is ( 0 , 9 8 ) .

Got questions? Get instant answers now!

For each of the following exercises, solve the equation for y in terms of x .

4 x + 2 y = 8

y = 4 2 x

Got questions? Get instant answers now!

2 x = 5 3 y

y = 5 2 x 3

Got questions? Get instant answers now!

5 y + 4 = 10 x

y = 2 x 4 5

Got questions? Get instant answers now!

For each of the following exercises, find the distance between the two points. Simplify your answers, and write the exact answer in simplest radical form for irrational answers.

( −4 , 1 ) and ( 3 , −4 )

d = 74

Got questions? Get instant answers now!

( 2 , −5 ) and ( 7 , 4 )

Got questions? Get instant answers now!

( 5 , 0 ) and ( 5 , 6 )

d = 36 = 6

Got questions? Get instant answers now!

( −4 , 3 ) and ( 10 , 3 )

Got questions? Get instant answers now!

Find the distance between the two points given using your calculator, and round your answer to the nearest hundredth.

( 19 , 12 ) and ( 41 , 71 )

d 62.97

Got questions? Get instant answers now!

For each of the following exercises, find the coordinates of the midpoint of the line segment that joins the two given points.

( −5 , −6 ) and ( 4 , 2 )

Got questions? Get instant answers now!

( −1 , 1 ) and ( 7 , −4 )

( 3 , 3 2 )

Got questions? Get instant answers now!

( −5 , −3 ) and ( −2 , −8 )

Got questions? Get instant answers now!

( 0 , 7 ) and ( 4 , −9 )

( 2 , −1 )

Got questions? Get instant answers now!

( −43 , 17 ) and ( 23 , −34 )

Got questions? Get instant answers now!

Graphical

For each of the following exercises, identify the information requested.

What are the coordinates of the origin?

( 0 , 0 )

Got questions? Get instant answers now!

If a point is located on the y -axis, what is the x -coordinate?

Got questions? Get instant answers now!

If a point is located on the x -axis, what is the y -coordinate?

y = 0

Got questions? Get instant answers now!

For each of the following exercises, plot the three points on the given coordinate plane. State whether the three points you plotted appear to be collinear (on the same line).

( 4 , 1 ) ( −2 , −3 ) ( 5 , 0 )

This is an image of a blank x, y coordinate plane with the x and y axes ranging from negative 5 to 5.
Got questions? Get instant answers now!

( −1 , 2 ) ( 0 , 4 ) ( 2 , 1 )

This is an image of a blank x, y coordinate plane with the x and y axes ranging from negative 5 to 5.


This is an image of an x, y coordinate plane with the x and y axes ranging from negative 5 to 5. The points (0,4); (-1,2) and (2,1) are plotted and labeled.

not collinear

Got questions? Get instant answers now!

( −3 , 0 ) ( −3 , 4 ) ( −3 , −3 )

This is an image of a blank x, y coordinate plane with the x and y axes ranging from negative 5 to 5.
Got questions? Get instant answers now!

Name the coordinates of the points graphed.

This is an image of an x, y coordinate plane where the x and y-axis range from negative 5 to 5. Three points are plotted: A, B, and C.

( −3 , 2 ) , ( 1 , 3 ) , ( 4 , 0 )

Got questions? Get instant answers now!

Name the quadrant in which the following points would be located. If the point is on an axis, name the axis.

a . ( −3 , −4 ) b . ( −5 , 0 ) c . ( 1 , −4 ) d . ( −2 , 7 ) e . ( 0 , −3 )

Got questions? Get instant answers now!

For each of the following exercises, construct a table and graph the equation by plotting at least three points.

y = 1 3 x + 2

x y
−3 1
0 2
3 3
6 4

This is an image of an x, y coordinate plane with the x and y axes ranging from negative 10 to 10.  The points (-3, 1); (0, 2); (3, 3) and (6, 4) are plotted and labeled.  A line runs through all these points.

Got questions? Get instant answers now!

2 y = x + 3

x y
–3 0
0 1.5
3 3

This is an image of an x, y coordinate plane with the x and y axes ranging from negative 10 to 10.  The points (-3, 0); (0, 1.5) and (3, 3) are plotted and labeled.  A line runs through all of these points.

Got questions? Get instant answers now!

Numeric

For each of the following exercises, find and plot the x- and y -intercepts, and graph the straight line based on those two points.

For each of the following exercises, use the graph in the figure below.

This is an image of an x, y coordinate plane with the x and y axes ranging from negative 5 to 5.  The points (-3, 4) and (5, 2) are plotted.  A line connects these two points.

Find the distance between the two endpoints using the distance formula. Round to three decimal places.

d = 8.246

Got questions? Get instant answers now!

Find the coordinates of the midpoint of the line segment connecting the two points.

Got questions? Get instant answers now!

Find the distance that ( −3 , 4 ) is from the origin.

d = 5

Got questions? Get instant answers now!

Find the distance that ( 5 , 2 ) is from the origin. Round to three decimal places.

Got questions? Get instant answers now!

Which point is closer to the origin?

( −3 , 4 )

Got questions? Get instant answers now!

Technology

For the following exercises, use your graphing calculator to input the linear graphs in the Y= graph menu.

After graphing it, use the 2 nd CALC button and 1:value button, hit enter. At the lower part of the screen you will see “x=” and a blinking cursor. You may enter any number for x and it will display the y value for any x value you input. Use this and plug in x = 0, thus finding the y -intercept, for each of the following graphs.

Y 1 = 3 x 8 4

x = 0           y = −2

Got questions? Get instant answers now!

For the following exercises, use your graphing calculator to input the linear graphs in the Y= graph menu.

After graphing it, use the 2 nd CALC button and 2:zero button, hit enter. At the lower part of the screen you will see “left bound?” and a blinking cursor on the graph of the line. Move this cursor to the left of the x -intercept, hit ENTER. Now it says “right bound?” Move the cursor to the right of the x -intercept, hit enter. Now it says “guess?” Move your cursor to the left somewhere in between the left and right bound near the x -intercept. Hit enter. At the bottom of your screen it will display the coordinates of the x- intercept or the “zero” to the y -value. Use this to find the x -intercept.

Note: With linear/straight line functions the zero is not really a “guess,” but it is necessary to enter a “guess” so it will search and find the exact x -intercept between your right and left boundaries. With other types of functions (more than one x -intercept), they may be irrational numbers so “guess” is more appropriate to give it the correct limits to find a very close approximation between the left and right boundaries.

Y 1 = −8 x + 6

x = 0.75       y = 0

Got questions? Get instant answers now!

Y 1 = 3 x + 5 4 Round your answer to the nearest thousandth.

x = 1.667       y = 0

Got questions? Get instant answers now!

Extensions

A man drove 10 mi directly east from his home, made a left turn at an intersection, and then traveled 5 mi north to his place of work. If a road was made directly from his home to his place of work, what would its distance be to the nearest tenth of a mile?

Got questions? Get instant answers now!

If the road was made in the previous exercise, how much shorter would the man’s one-way trip be every day?

15 −11 . =  3 .8 mi shorter

Got questions? Get instant answers now!

Given these four points: A ( 1 , 3 ) , B ( 3 , 5 ) , C ( 4 , 7 ) ,  and   D ( 5 , −4 ) , find the coordinates of the midpoint of line segments AB ¯ and CD ¯ .

Got questions? Get instant answers now!

After finding the two midpoints in the previous exercise, find the distance between the two midpoints to the nearest thousandth.

6 .0 42

Got questions? Get instant answers now!

Given the graph of the rectangle shown and the coordinates of its vertices, prove that the diagonals of the rectangle are of equal length.

This is an image of an x, y coordinate plane with the x and y axes ranging from negative 12 to 12.  The points (-6, 5); (10, 5); (-6, -1) and (10, -1) are plotted and labeled.  These points are connected to form a rectangle.  Dotted lines extend from each corner point to their opposite point.
Got questions? Get instant answers now!

In the previous exercise, find the coordinates of the midpoint for each diagonal.

Midpoint of each diagonal is the same point ( 2 , 2 ) . Note this is a characteristic of rectangles, but not other quadrilaterals.

Got questions? Get instant answers now!

Real-world applications

The coordinates on a map for San Francisco are ( 53 , 17 ) and those for Sacramento are ( 123 , 78 ) . Note that coordinates represent miles. Find the distance between the cities to the nearest mile.

Got questions? Get instant answers now!

If San Jose’s coordinates are ( 76 , −12 ) , where the coordinates represent miles, find the distance between San Jose and San Francisco to the nearest mile.

37 mi

Got questions? Get instant answers now!

A small craft in Lake Ontario sends out a distress signal. The coordinates of the boat in trouble were ( 49 , 64 ) . One rescue boat is at the coordinates ( 60 , 82 ) and a second Coast Guard craft is at coordinates ( 58 , 47 ) . Assuming both rescue craft travel at the same rate, which one would get to the distressed boat the fastest?

Got questions? Get instant answers now!

A man on the top of a building wants to have a guy wire extend to a point on the ground 20 ft from the building. To the nearest foot, how long will the wire have to be if the building is 50 ft tall?

A right triangle with its bottom left point sitting on the point (0,0).  The upper right hand corner is labeled (20,50).  The base has a length of 20 units and the triangle has a height of 50 units.

54 ft

Got questions? Get instant answers now!

If we rent a truck and pay a $75/day fee plus $.20 for every mile we travel, write a linear equation that would express the total cost y , using x to represent the number of miles we travel. Graph this function on your graphing calculator and find the total cost for one day if we travel 70 mi.

Got questions? Get instant answers now!

Questions & Answers

what is mutation
Janga Reply
what is a cell
Sifune Reply
how is urine form
Sifune
what is antagonism?
mahase Reply
classification of plants, gymnosperm features.
Linsy Reply
what is the features of gymnosperm
Linsy
how many types of solid did we have
Samuel Reply
what is an ionic bond
Samuel
What is Atoms
Daprince Reply
what is fallopian tube
Merolyn
what is bladder
Merolyn
what's bulbourethral gland
Eduek Reply
urine is formed in the nephron of the renal medulla in the kidney. It starts from filtration, then selective reabsorption and finally secretion
onuoha Reply
State the evolution relation and relevance between endoplasmic reticulum and cytoskeleton as it relates to cell.
Jeremiah
what is heart
Konadu Reply
how is urine formed in human
Konadu
how is urine formed in human
Rahma
what is the diference between a cavity and a canal
Pelagie Reply
what is the causative agent of malaria
Diamond
malaria is caused by an insect called mosquito.
Naomi
Malaria is cause by female anopheles mosquito
Isaac
Malaria is caused by plasmodium Female anopheles mosquitoe is d carrier
Olalekan
a canal is more needed in a root but a cavity is a bad effect
Commander
what are pathogens
Don Reply
In biology, a pathogen (Greek: πάθος pathos "suffering", "passion" and -γενής -genēs "producer of") in the oldest and broadest sense, is anything that can produce disease. A pathogen may also be referred to as an infectious agent, or simply a germ. The term pathogen came into use in the 1880s.[1][2
Zainab
A virus
Commander
Definition of respiration
Muhsin Reply
respiration is the process in which we breath in oxygen and breath out carbon dioxide
Achor
how are lungs work
Commander
where does digestion begins
Achiri Reply
in the mouth
EZEKIEL
what are the functions of follicle stimulating harmones?
Rashima Reply
stimulates the follicle to release the mature ovum into the oviduct
Davonte
what are the functions of Endocrine and pituitary gland
Chinaza
endocrine secrete hormone and regulate body process
Achor
while pituitary gland is an example of endocrine system and it's found in the Brain
Achor
what's biology?
Egbodo Reply
Biology is the study of living organisms, divided into many specialized field that cover their morphology, physiology,anatomy, behaviour,origin and distribution.
Lisah
biology is the study of life.
Alfreda
Biology is the study of how living organisms live and survive in a specific environment
Sifune
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College algebra' conversation and receive update notifications?

Ask