Introduction

Many real-life applications involve data that can be modeled by a linear equation. In this chapter you will write linear equations in various forms, look at parallel and perpendicular lines, graph scatter plots, and write a best-fit line for the data. You will first approximate a line of best fit and then use graphing calculators (or spreadsheets) to generate the regression equation of the line of best fit.

Lesson Objectives

After completing this lesson, you should be able to:

• write linear equations in two variables in various forms, including y = mx + b, Ax + By = C, and , given one point and the slope and given two points;
• write linear equations in two variables given a table of values, a graph, and a verbal description;
• write the equation of a line that contains a given point and is parallel to a given line;
• write the equation of a line that contains a given point and is perpendicular to a given line;
• write an equation of a line that is parallel or perpendicular to the X or Y axis and determine whether the slope of the line is zero or undefined;
• determine the slope of a line given a table of values, a graph, two points on the line, and an equation written in various forms, including y = mx + b, Ax + By = C, and ;
• calculate, using technology, the correlation coefficient between two quantitative variables and interpret this quantity as a measure of the strength of the linear association;
• compare and contrast association and causation in real-world problems;
• write, with and without technology, linear functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems; and
• write a formula for the  term of arithmetic and geometric sequences, given the value of several of their terms.

Materials Needed

• Textbook: Big Ideas Math, Algebra 1
• Spiral notebook for notes
• Graphing calculator

How to Proceed

1. Read the Introduction and Objectives for this lesson. They will give you an idea of the major concepts you need to watch for as you read, as well as the kinds of skills you will be expected to have at the end of the lesson.
   
   
2. Survey pages 158-215 in your textbook. (Skim and/or look at the title, the introduction, the headings and subheadings, the graphics, and the important terms. The Chapter Review on pages 210-212 is a good place to see an overview of what you’ll be learning in Lesson Four.)
   
   
3. Read the assigned pages in your textbook for each section of this lesson. The assigned textbook readings are given at the beginning of each Section Summary.
   
   
4. Take notes on the assigned pages for each section. Pay attention to the list of key words in each section. The key words are important and should be remembered for future reference.
   
   
5. Read the Section Summaries on the course homepage. They will help you to understand what you read in the textbook. Read and study all examples given in the textbook.
   
   
6. Complete the Section Assignments neatly on paper to be scanned and saved as a PDF (see "Textbooks and Materials" in the Course Introduction). Show every step and box your answers as shown in the Sample Lesson Submission in the Resources section of this course. When you have completed all of the assignments, save them as a single PDF and upload your work using the Lesson Four: Assignment Upload.
   
   
7. Review your notes briefly every day until you complete the course. After you have finished this lesson, you may proceed to Lesson Five.

Before You Begin

Before you begin this chapter, look through the whole chapter to become acquainted with what will be covered. Remember that each chapter has two sections labeled "What Did You Learn?". This part of the book lists the core vocabulary and core concepts. Make sure that you have all of the core vocabulary and core concepts written in your notes and defined. You may also want to add some examples.

Now look at pages 159 and 160. Work through Maintaining Mathematical Proficiency and Mathematical Thinking. This will serve as a review of some skills and topics that you should know and will also need for this chapter.

The first coordinate in an ordered pair is the x-coordinate. Its sign indicates whether the point is left or right of the y-axis. The second coordinate is the y-coordinate, and its sign indicates whether the point is above or below the x-axis. Review the positions of the four quadrants. They are numbered in the counterclockwise direction, beginning with the upper right quadrant, Quadrant I.

Also remember to not skip steps when evaluating expressions. Both sides of an equation must remain equal. So each operation must be performed on both sides of the equation. If you divide the left side by 2, you must also divide the right side by 2. This will help you not make careless mistakes.

Check your answers for Maintaining Mathematical Proficiency (page 159) in the Selected Answers section of your textbook, beginning on page A1.

On page 160, you are using the problem-solving strategy of solving a simpler form of the problem. This is a good strategy to practice. Answers to Monitoring Progress are below.

Answers to Monitoring Progress (page 160)

1. $9.40 per hour
2. 26.2 mi/gal
3. about 8.8 h