Math 10C Module 6: Lesson 3

Module 6: Linear Equations

Lesson 3 Summary

In this lesson you investigated the following questions:

  • How can you determine the relative orientation of a pair of lines by examining their slopes?

  • How can knowledge of mathematical relationships between parallel and perpendicular lines be applied to problem-solving situations?

In this lesson you examined the relationship between the slopes of parallel lines and between the slopes of perpendicular lines. You discovered that the slopes of parallel lines are equal. Conversely, if two lines with different y-intercepts have the same slope, they are parallel to one another. You also learned that the slopes of perpendicular lines are negative reciprocals of each other.

For example, if the slope of one line is then the slope of a line that is perpendicular to the first is βˆ’2. The product of a pair of negative reciprocals is βˆ’1.

The converse statement is also true: If the slopes of two lines are negative reciprocals of each other, then the lines are perpendicular to each other.

In the last lesson you learned how to use a line’s slope and points to determine its equation.

In this lesson you continued to practise writing linear equations. You were not always given information about the slope and points directly. In this lesson you worked with a partner to develop strategies for extracting the information that you need to construct equations. These strategies may have included rearranging an equation in order to uncover its slope or its y-intercept. As well, you may have chosen to graph a line in order to help you determine its properties. Knowing the information that you need is a vital first step in solving a mathematical problem. The second step is to recognize the information that can be provided by the problem constraints.

In the next lesson you will learn how to apply linear equations to problem-solving situations. You will combine all of the concepts that you have learned in this module. You will use function notation to model linear relations, construct equations based on given information, and use those equations to determine solutions.

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