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Applications of Linear Relations

Source: LightBulb Crumped Paper - ThomasVogel/iStock/Getty Images

Problem Solving

Throughout previous lessons on Linear Relations, we have:

  • introduced properties of linear relations,
  • made connections between representations,
  • developed formulas and equations, and
  • solved specific problems.

Now that you are equipped with a variety of tools, different strategies, and a solid foundational knowledge of linear relations, we will look at multiple problems that encompass the ideas presented throughout the Linear Relations units.

Children with light-bulb helmets on their heads.

A chess board with pieces.

Sources: Children Wearing LightBulbs - RichVintage/iStock/Getty Images; 
Chess Board and Pieces - traviswolfe/iStock/Getty Images

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Lesson Goals

  • Solve problems involving linear relations represented in different forms.
  • Determine a point of intersection graphically, and explain the meaning within a given context. 
  • Identify and explain restrictions on variables within a given context.

Try This

A company rents hoverboards and electric scooters. The relationship between cost and time traveled for each rental is linear. For a hoverboard, this relationship is represented in the table. For an electric scooter, the relationship is represented in the graph. If Henry has \($5\) to spend, which mode of transportation will get him the rental for the most amount of time? 

Hoverboard Rental

Time (min) Cost \(($)\)
\(2\) \($1.30\)
\(4\) \($1.60\)

Electric Scooter Rental

A straight line passes through points (0, 0.5) and (4, 1.5). The x-axis represents time starting at 0. The y-axis represents cost.