Lesson 2: The Equation of a Line

Explore 2

Determining the Equation of a Line: Given Two Points

In mathematics, there are many different ways of solving the same question. It is important that you develop problem-solving strategies that suit you—no two people think in exactly the same way..

Try This 2
Complete the following questions in your course folder ( binder).

TT 2.  a.Develop a strategy for writing the equation of a line when given two points. (Hint: Is there a way to determine the slope of the line?)       
        b.   Demonstrate how this strategy can be applied to the following exercise. Write the equation of a line that passes through the points (–2, 1) and (1, 7). Express your answer in slope-intercept form as well as general form.

  Watch and Listen

Watch the “Linear Equation Given Two Points” video, and compare your strategy in TT 2 to the strategy suggested in the video. Also, see if your answers match the answers presented in the video.

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Try This 3

 Based on what you have seen in the video clip, complete TT 3 in your course folder (binder).
Answer the questions based on what you have seen in the video titled “Linear Equation Given Two Points” and your own results.

TT 3. a.   How did your strategy compare with the strategy presented in the video? Were they exactly the same? If so, what is your rationale for using this strategy? If not, how did you arrive at the correct answer?

        b.   Two points are given in the question, but only one point was used to determine the equation of the line. Did you use the same point as was used in the video? If so, try the other point to see if it would yield the same equation. If not, what conclusions can you make about which point should be used?

Possible TT3 Answers

  Read

Go to your textbook to work through an example that demonstrates how to determine the equation of a line when given two points on the line.

Use the link titled “Finding the Equation of a Line” to practice writing equations of linear functions. They start out very simple and then get more complicated. No solutions are provided, just a mark, but it is good practice.

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 Watch and Listen

It’s play time! 

Click on “Deep Sea Diver” . You will navigate the depths of the sea as a scuba diver. Collect the gems and evade the jellyfish, sharks, and whales. Don’t forget to go to the buoys at the surface for air!
In order to progress through the levels, you will have to answer multiple choice questions correctly. All of these questions deal with the concepts learned in this lesson. You will receive rewards to help you each time you answer a question correctly. Good luck!
Hint: In this game, you will encounter the expression standard form. You may want to review your glossary terms from Module 5: Lesson 4 to recall what this means.

  Self-Check

Now that you have worked through an interactive lesson and played a game relating to writing linear equations, here is an opportunity for you to demonstrate what you have learned. For each of the following questions, show the steps that you would follow to obtain the equation. You may use either an algebraic or graphical approach.
SC 5. In slope-intercept form, write the equation of the line that passes through the following points:

1. (0, 4) and (2, 0)
2. (2, 4) and (6, 6)
3. (−2, 1) and (1, −4)

Compare your answers.

  Try This 4

Complete the following in your binder.

Foundations and Pre-calculus Mathematics 10 (Pearson)
TT 4.a.  Complete “Exercises” question 11 on page 372.
        b.   Complete “Review” questions 18 and 19 on pages 389 and 390.
Use the link below to check your answers to Try This 4.
Possible TT4 Solutions