Applications of linear relations - Linear Functions

Applications of linear relations

Let's put the linear functions in words! It's not hard to find things with linear relations around us. We will show you how to solve linear relationship word problems.

Basic Concepts
Representing patterns in linear relations
Reading linear relation graphs
Solving linear equations by graphing

Related Concepts
Applications of linear equations
Applications of quadratic functions

Lessons

- a)
  How to turn a word problem into an equation?
  • ex. 1: "revenue" problem
  • ex. 2: "area" problem

Applications of linear relations

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AlgebraRepresenting patterns in linear relations

AlgebraReading linear relation graphs

AlgebraSolving linear equations by graphing

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Representing patterns in linear relations

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Intro Lesson

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Don't just watch, practice makes perfect

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Lessons

Intro Lesson

a)

How to turn a word problem into an equation? • ex. 1: "revenue" problem • ex. 2: "area" problem

1.

The value VVV of a classic toy car, in dollars, is given by V+15t=350V + 15t = 350V+15t=350, where ttt is the age of the car. If the car was bought new 5 years ago, graph the equation and estimate the value of the car 6 years from now.

2.

The cost CCC, in dollars, of renting a hall for the prom is given by the formula C(n)=500+4nC(n) = 500 + 4nC(n)=500+4n, where nnn is the number of students attending the prom. Calculate the cost of renting the hall if 70 students attend.

3.

Sam completes a puzzle in time ttt (mins) is related to number of tries (nnn). The resulting equation is t=30−45nt = 30 - {4 \over 5}nt=30−54​n Graph the equation and estimate the time it takes him to do the puzzle on his 15th15^{th}15th try.

4.

A game rental store charges $15.00 to rent the console and the game and $3.00 per additional hour. Write the linear equation. Determine the cost of renting for 15 hours. Determine the hours if the cost was $150.

5.

In 1970 the population of Andyland city was 900,000, in 1995 the population of the same city had grown to 1,500,000. i) Find the average rate of change for the population of this city from 1970 to 1995. ii) Predict how many people will live in this city in 2015.

6.

A car repair shop charges an hourly rate plus a fixed amount. One hour costs $70, and four hours costs $160. i) Determine the hourly rate. ii) Write the equation that shows the total cost (CCC) in terms of number of hours (HHH) and the fixed cost (FFF). iii) Domain and Range.

7.

Jack has two options when renting his car for the vacation: Option A: $50 per day, and no extra charge per kilometre. Option B: $35 per day, and 15 cents per kilometre. i) Graph the options AAA & BBB ii) How many kilometres must Jack travel to make option AAA the cheapest rate?

Applications of linear relations

Don't just watch, practice makes perfect.

We have over 1850 practice questions in Algebra for you to master.

Algebra
Representing patterns in linear relations

Algebra
Reading linear relation graphs

Algebra
Solving linear equations by graphing

or

How to turn a word problem into an equation?
• ex. 1: "revenue" problem
• ex. 2: "area" problem

The value $V$ of a classic toy car, in dollars, is given by $V + 15t = 350$ , where $t$ is the age of the car. If the car was bought new 5 years ago, graph the equation and estimate the value of the car 6 years from now.

The cost $C$ , in dollars, of renting a hall for the prom is given by the formula $C(n) = 500 + 4n$ , where $n$ is the number of students attending the prom. Calculate the cost of renting the hall if 70 students attend.

Sam completes a puzzle in time $t$ (mins) is related to number of tries ( $n$ ). The resulting equation is $t = 30 - {4 \over 5}n$ Graph the equation and estimate the time it takes him to do the puzzle on his $15^{th}$ try.

In 1970 the population of Andyland city was 900,000, in 1995 the population of the same city had grown to 1,500,000.
i) Find the average rate of change for the population of this city from 1970 to 1995.
ii) Predict how many people will live in this city in 2015.

A car repair shop charges an hourly rate plus a fixed amount. One hour costs $70, and four hours costs $160.
i) Determine the hourly rate.
ii) Write the equation that shows the total cost ( $C$ ) in terms of number of hours ( $H$ ) and the fixed cost ( $F$ ).
iii) Domain and Range.

Jack has two options when renting his car for the vacation:
Option A: $50 per day, and no extra charge per kilometre.
Option B: $35 per day, and 15 cents per kilometre.
i) Graph the options $A$ & $B$
ii) How many kilometres must Jack travel to make option $A$ the cheapest rate?