Math 10C Module 6: Lesson 4

Module 6: Linear Equations

Lesson 4 Summary

In this lesson you investigated the following questions:

  • How are the fixed and variable elements of a problem related to the linear equation y = mx + b?

  • How do you apply techniques and concepts learned in this module to solve problems?

In this final lesson of Module 6 you tackled applications of linear relations. You used what you learned in the previous lessons of this module to solve linear problems. You interpreted linear functions expressed in function notation. You learned that a linear equation has a fixed term and a variable term corresponding to the mx-term and the b-term, respectively, in the equation y = mx + b. The fixed and variable terms can be used to translate descriptions of linear relations into equations. You worked through interactive lessons, studied examples, and tried different exercises to practise constructing and using equations to model linear situations.

In the Math Lab you gathered data by counting the beats to a favourite song. You then constructed an equation to model the linear relation between beats and elapsed time. Through this activity you may have learned to appreciate a systematic approach to mathematical problem solving. This approach involves breaking the solution into smaller parts including the following:

  • identify and assign variables

  • sketch a graph

  • construct an equation

  • use the equation to predict other values

Strategies may differ slightly but each component listed above is essential to a complete solution.

In the next module you will consider systems of two linear equations. You will solve systems of equations in various ways, from graphical methods to algebraic methods. Your mastery of the concepts in this module will serve as a strong foundation as you move into the remaining lessons in this course.

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