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Access this online resource for additional instruction and practice with linear function models.

Key concepts

  • We can use the same problem strategies that we would use for any type of function.
  • When modeling and solving a problem, identify the variables and look for key values, including the slope and y -intercept. See [link] .
  • Draw a diagram, where appropriate. See [link] and [link] .
  • Check for reasonableness of the answer.
  • Linear models may be built by identifying or calculating the slope and using the y -intercept.
    • The x -intercept may be found by setting y = 0 , which is setting the expression m x + b equal to 0.
    • The point of intersection of a system of linear equations is the point where the x - and y -values are the same. See [link] .
    • A graph of the system may be used to identify the points where one line falls below (or above) the other line.

Section exercises

Verbal

Explain how to find the input variable in a word problem that uses a linear function.

Determine the independent variable. This is the variable upon which the output depends.

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Explain how to find the output variable in a word problem that uses a linear function.

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Explain how to interpret the initial value in a word problem that uses a linear function.

To determine the initial value, find the output when the input is equal to zero.

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Explain how to determine the slope in a word problem that uses a linear function.

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Algebraic

Find the area of a parallelogram bounded by the y -axis, the line x = 3 , the line f ( x ) = 1 + 2 x , and the line parallel to f ( x ) passing through ( 2 , 7 ) .

6 square units

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Find the area of a triangle bounded by the x -axis, the line f ( x ) = 12 1 3 x , and the line perpendicular to f ( x ) that passes through the origin.

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Find the area of a triangle bounded by the y -axis, the line f ( x ) = 9 6 7 x , and the line perpendicular to f ( x ) that passes through the origin.

20.01 square units

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Find the area of a parallelogram bounded by the x -axis, the line g ( x ) = 2 , the line f ( x ) = 3 x , and the line parallel to f ( x ) passing through ( 6 , 1 ) .

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For the following exercises, consider this scenario: A town’s population has been decreasing at a constant rate. In 2010 the population was 5,900. By 2012 the population had dropped 4,700. Assume this trend continues.

Predict the population in 2016.

2,300

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Identify the year in which the population will reach 0.

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For the following exercises, consider this scenario: A town’s population has been increased at a constant rate. In 2010 the population was 46,020. By 2012 the population had increased to 52,070. Assume this trend continues.

Predict the population in 2016.

64,170

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Identify the year in which the population will reach 75,000.

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For the following exercises, consider this scenario: A town has an initial population of 75,000. It grows at a constant rate of 2,500 per year for 5 years.

Find the linear function that models the town’s population P as a function of the year, t , where t is the number of years since the model began.

P ( t ) = 75 , 000 + 2500 t

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Find a reasonable domain and range for the function P .

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If the function P is graphed, find and interpret the x - and y -intercepts.

(–30, 0) Thirty years before the start of this model, the town had no citizens. (0, 75,000) Initially, the town had a population of 75,000.

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Questions & Answers

sin theta=3/4.prove that sec square theta barabar 1 + tan square theta by cosec square theta minus cos square theta
Umesh Reply
I want to know trigonometry but I can't understand it anyone who can help
Siyabonga Reply
Yh
Idowu
which part of trig?
Nyemba
functions
Siyabonga
trigonometry
Ganapathi
differentiation doubhts
Ganapathi
hi
Ganapathi
hello
Brittany
Prove that 4sin50-3tan 50=1
Sudip Reply
f(x)= 1 x    f(x)=1x  is shifted down 4 units and to the right 3 units.
Sebit Reply
f (x) = −3x + 5 and g (x) = x − 5 /−3
Sebit
what are real numbers
Marty Reply
I want to know partial fraction Decomposition.
Adama Reply
classes of function in mathematics
Yazidu Reply
divide y2_8y2+5y2/y2
Sumanth Reply
wish i knew calculus to understand what's going on 🙂
Dashawn Reply
@dashawn ... in simple terms, a derivative is the tangent line of the function. which gives the rate of change at that instant. to calculate. given f(x)==ax^n. then f'(x)=n*ax^n-1 . hope that help.
Christopher
thanks bro
Dashawn
maybe when i start calculus in a few months i won't be that lost 😎
Dashawn
what's the derivative of 4x^6
Axmed Reply
24x^5
James
10x
Axmed
24X^5
Taieb
Thanks for this helpfull app
Axmed Reply
secA+tanA=2√5,sinA=?
richa Reply
tan2a+tan2a=√3
Rahulkumar
classes of function
Yazidu
if sinx°=sin@, then @ is - ?
NAVJIT Reply
the value of tan15°•tan20°•tan70°•tan75° -
NAVJIT
0.037 than find sin and tan?
Jon Reply
cos24/25 then find sin and tan
Deepak Reply

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Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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