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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

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
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John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
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hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
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Source:  OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
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