Complete the table of values for the linear function 3x+2y=−6.
Before completing the table of values, solve the given function in terms of ‘y’. This step is not necessary, but it does simplify the calculations.
3x+2y=−63x−3x+2y=−3x−6 2y=−3x−6 2y2=−3x2−62 y=−3x2−3
y=−3x2−3y=−3(−4)2−3y=−3x2−3y=−3(2)2−3y=122−3y=6−3y=3y=−62−3y=−3−3y=−6y=−3x2−3y=−3(0)2−3y=−3x2−3y=−3(6)2−3y=0−3y=−3y=−182−3y=−9−3y=−12
y=−32x−3
X Y
−4 3
0 −3
2 −6
6 −12
Example B
Use technology to create a table of values for the linear function f(x)=−12x+4.
When the table is set up, you choose the beginning number as well as the pattern for the numbers in the table. In this table, the beginning value for ‘x’ is –2 and the difference between each number is +2. The table is consecutive, even numbers. When consecutive numbers are used as the input numbers (x−values), there is a definite pattern in the output numbers (y−values). This will be expanded upon in a later lesson.
Example C
Complete the table of values for the following linear function, and use those values to graph the function.
x−2y=4x−x−2y=−x+4−2y=−x+4−2y−2=−x−2+4−2y=12x−2
y=12x−2 y=12(−4)−2 y=−2−2y=−4 y=12x−2 y=12(0)−2 y=0−2y=−2 y=12x−2 y=12(2)−2 y=1−2y=−1 y=12x−2 y=12(6)−2 y=3−2y=1
y=12x−2
X Y
−4 −4
0
Vocabulary
Linear Function
A linear function is a relation between two variables, usually x and y, in which each value of the independent variable (x) is mapped to one and only one value of the dependent variable (y).
Guided Practice
1. Complete the following table of values for the linear function 3x−2y=−12
3x−2y=−12
X Y
−6
−4
0
6
2. Use technology to complete a table of values for the linear function 2x−y=−8 and use the coordinates to draw the graph.
3. A local telephone company charges a monthly fee of $25.00 plus $0.09 per minute for calls within the United States. If Sam talks for 200 minutes in one month, calculate the cost of his telephone bill.
Answers
1. 3x−2y=−12 Solve the equation in terms of the variable ‘y’.
3x−3x−2y=−3x−12−2y=−3x−12−2y−2=−3x−2−12−2
y=32x+6 Substitute the given values for ‘x’ into the function.
y=32x+6 y=32(−6)+6 y=−9+6y=−3 y=32x+6 y=32(−4)+6 y=−6+6y=0 y=32x+6 y=32(0)+6 y=0+6y=6 y=32x+6 y=32(6)+6 y=9+6y=15
3x−2y=−12
X Y
−6 −3
−4 0
0 6
6 15
2. 2x−y=−8 To enter the function into the calculator, it must be in the form y=–––––––––––.
Solve the function in terms of the letter ‘y’.
2x−y=−8y=2x+82x−2x−y=−2x−8−y=−2x−8−y−1=−2x−1−8−1
The graph can also be done using technology. The table can be used to set the window.
3. y=0.09x+25 Write a linear function to represent the word problem.
yy=0.09(200)+25=$43.00Substitute the time of 200 minutes for the variable ‘x′.
The cost of Sam’s telephone bill is $43.00.
Summary
In this lesson, you have learned how to evaluate a linear function with given values. These values were given in table form. The table was completed by entering the values obtained from substituting the given values for ‘x’ into the linear function. These values were the coordinates of points that were located on the graph of the linear function. The points were used to draw the graph on a Cartesian plane.
The lesson then extended into the world of technology. The graphing calculator was used to create a table of values as well as to create the graph of the function. The more you practice the keystrokes for performing these tasks on the calculator, the more efficient you will become.
Problem Set
Solve each of the following linear functions in terms of the variable ‘y’.
2x−3y=18
4x−2y=10
3x−y=8
5x+3y=−12
3x−2y−2=0
For each of the following linear functions, create a table of values that contains four coordinates:
y=−4x+5
5x+3y=15
4x−3y=6
2x−2y+2=0
2x−3y=9
For each of the linear functions, complete the table of values and use the values to draw the graph.
y=−2x+1
x−3015y
x=2y−3
x−4026y
3x+2y=8
x−6−204y
4(y−1)=12x−7
x−2037y
12x+13y=6
x04610y
Using technology, create a table of values for each of the following linear functions. Using technology, graph each of the linear functions.
y=−2x+3
y=−12x−3
y=43x−2
Mr. Red is trying to estimate the cost of renting a car to go on vacation. He has contacted a rental agency and has obtained the following information. The agency charges a daily rate of $78.00 for the vehicle plus 45 cents per mile. If Mr. Red has $350 set aside for travel, create a table of values that will give him approximate distances that he can travel with this rental car.
Graphing a Linear Function Using the X- and Y-Intercepts
Objectives
The lesson objectives for Graphing a Linear Function Using the X- and Y-Intercepts are:
Understanding the x- and y−intercepts
Determining the x- and y−intercepts for a given linear function
Using the x- and y−intercepts to graph the linear function
this isnt my work but hopefully this helps i did the best i could given th info you gave me
The winds in a microburst are _______. If a tornado causes considerable damage with wind speeds of 111 to 135 miles per hour, it is classified as _______ on the Enhanced Fujita Scale. This type of major storm is called a/an _______, and it is driven primarily by the Coriolis effect. The weather pattern that stays over one area for an extended period of time is known as _______. Respond to the following based on your reading. What are the two types of downbursts, and how are they different? How is a funnel cloud different from a tornado? List the various stages in the formation of a tropical cyclone or hurricane, in order. Why does a hurricane begin to dissipate after it makes landfall? Explain how the heat index and the wind chill index are similar and different. What type of severe weather prevents sweat from evaporating to cool down bodies?
Answer:
1.straight
2.EF-2
3.hurricane/tropical cyclone
4.recurrent weather
5.heat wave
6.The two types of downbursts are macrobursts and microbursts. A macroburst affects an area that's greater than 2.5 miles across. A microburst affects an area that's less than 2.5 miles across.
7.A funnel cloud forms as a spinning column of air that descends from a thundercloud. However, a funnel cloud doesn't become a tornado until it actually touches the ground. Once it touches the ground, where it begins to pick up dust and debris, it becomes a tornado.
8.The stages of tropical cyclone, or hurricane, formation are 1) tropical disturbance, 2) tropical depression, 3) tropical storm, and 4) tropical cyclone.
9.Tropical cyclones, such as hurricanes, are fueled by warm ocean waters. Once they make landfall, they lose this fuel source and begin to lose strength.
10.The heat index and the wind chill index are similar because both consider other factors that affect how air temperature feels. The heat index considers relative humidity in relation to air temperature. Higher humidity makes air temperatures feel hotter. The wind chill index considers wind speed in relation to air temperature. Higher wind speeds make air temperatures feel colder.
Explanation:
Answer:
EF-2
hurricane/tropical cyclone
recurrent weather
The two types of downbursts are macrobursts and microbursts. A macroburst affects an area that's greater than 2.5 miles across. A microburst affects an area that's less than 2.5 miles across.
A funnel cloud forms as a spinning column of air that descends from a thundercloud. However, a funnel cloud doesn't become a tornado until it actually touches the ground. Once it touches the ground, where it begins to pick up dust and debris, it becomes a tornado.
Tropical cyclones, such as hurricanes, are fueled by warm ocean waters. Once they make landfall, they lose this fuel source and begin to lose strength.
The heat index and the wind chill index are similar because both consider other factors that affect how air temperature feels. The heat index considers relative humidity in relation to air temperature. Higher humidity makes air temperatures feel hotter. The wind chill index considers wind speed in relation to air temperature. Higher wind speeds make air temperatures feel colder.
Heat waves—Heat waves can be very dangerous when accompanied by high humidity. The human body depends on evaporation of sweat to cool itself down on hot days. When humidity levels are high, the rate of evaporation slows down. Consequently, it becomes harder for the body to cool itself and much easier for the body to overheat.
A copy machine makes 32 copies per minute. How long does it take to make 184 copies?
Answer:
5.75 mins
Explanation:
184/32=5.75
It takes 5.75 minutes, or slightly over 5 minutes and 45 seconds, to make 184 copies on a machine that makes 32 copies per minute.
Explanation:To calculate the time needed to make 184 copies with a copy machine that makes 32 copies per minute, you perform a division operation. Divide the total number of copies (184) by the number of copies made per minute (32).
184 ÷ 32 = 5.75 minutes.
This means it takes 5.75 minutes to make 184 copies. However, in practical scenarios, a copy machine cannot make a fraction of a copy so the total time will be just slightly over 5 minutes and 45 seconds as you can't have part of a minute in actual timing.
The PSAT includes which of the following sections
A) social studies, math, and English
B) English, math, and science
C) Evidence-base reading, writing and language, and math
D) English, math, and humanities
'Evidence-base reading, writing and language and maths' includes in PSAT.
Option: C
Explanation:
PSAT- Preliminary Scholastic Aptitude Test is a rehearsal test for the students who are willing to take a SAT to get into a college with a scholarship. This test consists of two sections- Evidence Based reading, writing and language and mathematics. The reading test has 47 Multiple choice Questions for which the time limit is 60 minutes that includes comprehension, command of evidence, analytical skills and vocabulary in context. Then, comes the writing and language test which has 44 Multiple choice Questions with 35 minutes time limit, which consists vocabulary in context, tests grammar and editing skills of a student. At last, the mathematics section 48 questions in which most are Multiple choice Questions and others are solvable problems; it has a time limit of 70 minutes and contains geometry, tests algebra I and II, and some trigonometry questions.
Answer:
c is the answer
Explanation:
Over the course of the passage, the main focus shifts from
A- a description of the locale to a broader discussion of principles.
B- a humorous anecdote to a position on a popular u.s. debate
C- an analysis of the king’s situation to a analysis of an unemployed person’s
D- jefferson’s experiences in France to Madison’s experiences in the US
Answer:
A- a description of the locale to a broader discussion of principles.
Explanation:
In this text, we see that the author is taking a walk when he encounters an old woman in his path. As he meets the woman, he discovers that she is a local, and wanting to lean more about the culture he is in, they engage in a conversation about the setting they are in and the local culture. This superficial description of the setting leads to a broader discussion of more philosophical principles, particularly on the subject of economy.
If physical energy can be turned into thermal energy how hard do I have to punch a chicken to cook it
might as well kill the chicken with your punch so you can just cook it
the term that best exemplifies the freedom to spend your money the way you want is
Answer:
Explanation:
It is financial stability apex
Answer:
financial stability
Explanation: