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Introduction to Linear Relations — Part 2

Source: Hour Glass - artisteer/iStock/Getty Images

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  • We previously introduced the idea of a linear relation through patterning with tiles and building blocks.

Sources: Running - FatCamera/iStock/Getty Images; Cycling - claudio.arnese/iStock/Getty Images 

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Lesson Goals

  • Define the terms initial value and rate of change.
  • Given a linear relation, identify or calculate the initial value and rate of change from scenario descriptions, table of values and graphs, then use the values to develop a corresponding equation. 
  • Calculate first differences from a table of values and use this concept to determine if a relation is linear or non-linear.

Try This!

Lex was chatting with his friends Thomas and Mike. He was wondering how much it will cost him to take a taxi from his house to work, a total of \(12\) km. Thomas and Mike both recently took a taxi from the same company which charged an initial fee and also a constant rate per km travelled. Neither can remember how much the rates were but both of them still have their receipts with the total cost of the ride.

  • Thomas travelled \(10\) km and paid \($24.50\).

  • Mike travelled \(15\) km and paid \($35.00\).

How much will Lex pay to travel a distance of \(12\) km?