Lesson 4: General Form and Slope-Point Form

Module 5: Linear Functions

Lesson 4: General Form and Slope-Point Form

Focus

In the Summer Olympics, aquatic disciplines include swimming, diving, synchronized swimming, and water polo.

 

Consider the similarities and differences between synchronized swimming and relay swimming. Both competitions take place in a swimming pool and both involve teams of competitors. However, Olympic synchronized swimming is not open to men, whereas the relay events involve teams of women as well as teams of men.

Also, synchronized swimming is a judged competition where teams earn scores, whereas relay swimming is a race. In other words, the relay race is based on fastest times while synchronized swimming is based on both technical and aesthetic merits. The relay swimmer will adopt the most practical form to achieve the quickest time; the synchronized swimmer will work with her teammates to execute a performance that includes all the required components in a creative and artistic manner.

In mathematics you will also find different forms to express a linear function. In Lesson 3 you learned about the slope-intercept form. You will recall that this form is practical for obtaining the slope and y-intercept of a linear function. You may also recall how it was useful for graphing.

In this lesson you will learn how to express a linear function in other forms and from one form to the other. Just as some people prefer the excitement of relay competition and others enjoy the artistry of synchronized swimming, you may prefer to use some forms of linear functions for graphing and others for determining points and slopes.

Outcomes

At the end of this lesson, you will be able to

• express a linear relation in different forms and compare the graphs

• rewrite a linear relation in either slope-intercept or general form

• identify equivalent linear relations from a set of linear relations

Lesson Questions

• How are the general, slope-intercept, and slope-point forms different from each other?

• Why are there multiple ways of expressing linear functions?

Assessment

As you work through each lesson, complete all the questions and learning activities in your binder using paper and pencil, clearly labeling your work (they refer to this as your course folder). These include the Are you Ready, Try This, Share and Self Check questions. Check your work if answers are provided. Remember that these questions provide you with the practice and feedback that you need to successfully complete this course.
Once you have completed all of the learning activities, take the Lesson Quiz. This is the assessment for each lesson and is located under the Activities block on the left in moodle or under the Assess tab.

** Note – Share questions may have to be done on your own depending on your learning situation**

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