## Sloping and Intersecting a Linear Function

### Johnny WolfeSanta Rosa District Schools

#### Description

This lesson discusses graphing, slope, x-intercept and y-intercept.

#### Objectives

The student selects the appropriate operation to solve problems involving addition, subtraction, multiplication, and division of rational numbers, ratios, proportions, and percents, including the appropriate application of the algebraic order of operations.

Understands and explains the effects of addition, subtraction, multiplication and division on real numbers, including square roots, exponents, and appropriate inverse relationships.

The student identifies and plots ordered pairs in all four quadrants of a rectangular coordinate system (graph) and applies simple properties of lines.

The student describes a wide variety of patterns, relationships, and functions through models, such as manipulatives, tables, graphs, expressions, equations, and inequalities.

Describes, analyzes and generalizes relationships, patterns, and functions using words, symbols, variables, tables and graphs.

#### Materials

- Overhead transparencies (if examples are to be worked on overhead) for Sloping and Intersecting a linear Function (see attached file).

- Graph paper.

- Sloping and Intersecting a Linear Function Examples (see attached file).

- Sloping and Intersecting a Linear Function Worksheet (see attached file).

- Sloping and Intersecting a Linear Function Checklist (see attached file).

#### Preparations

1. Prepare transparencies (if teacher uses overhead for examples) for Sloping and Intersecting a linear Function Examples (see attached file).

2. Have marking pens (for overhead).

3. Have graphing paper.

4. Have Sloping and Intersecting a linear Function Examples (see attached file) prepared and ready to demonstrate to students.

5. Have enough copies of Sloping and Intersecting a linear Function Worksheet (see attached file) for each student.

6. Have enough copies of Sloping and Intersecting a linear Function Checklist (see attached file) for each student.

#### Procedures

Prior Knowledge: Students should be familiar with basic operation skills such as addition, subtraction, multiplication, division, exponents, fractions, decimals and solving equations. Note: This lesson does not address the following: square roots, exponents, and appropriate inverse relationships; ratios, proportions or percents; inequalities. This lesson contains a checklist to assist the teacher in determining which students need remediation. The sole purpose of this checklist is to aide the teacher in identifying students that need remediation.

1. Introduce students to a typical linear equation (see # 1 on attached file Sloping and Intersecting a Linear Function Examples). Answer student questions and comments.

2. Describe what constitutes a linear equation (see # 2 on attached file Sloping and Intersecting a Linear Function Examples). Answer student questions and comments.

3. Describe the difference between a linear and nonlinear equation (see # 3 on attached file Sloping and Intersecting a Linear Function Examples). Answer student questions and comments.

4. Describe the standard form of a linear equation (see # 4 on attached file Sloping and Intersecting a Linear Function Examples). Answer student questions and comments.

5. Work example 5 (see attached file Sloping and Intersecting a linear Function Examples). Answer student questions and comments.

6. Describe the process of graphing a linear equation (see # 6 on attached file Sloping and Intersecting a linear Function Examples). Answer student questions and comments.

7. Work example 7 (see attached file Sloping and Intersecting a linear Function Examples). Answer student questions and comments.

8. Work example 8 (see attached file Sloping and Intersecting a linear Function Examples). Answer student questions and comments.

9. Work example 9 (see attached file Sloping and Intersecting a linear Function Examples). Answer student questions and comments.

10. Work example 10 (see attached file Sloping and Intersecting a linear Function Examples). Answer student questions and comments.

11. Give an example of a nonlinear equation (see # 11 on attached file Sloping and Intersecting a linear Function Examples). Answer student questions and comments.

12. Give two special case examples of straight lines (see # 12 on attached file Sloping and Intersecting a linear Function Examples). Answer student questions and comments.

13. Discuss the definition of a linear function (see # 13 on attached file Sloping and Intersecting a linear Function Examples). Answer student questions and comments.

14. Describe a constant function (see # 14 on attached file Sloping and Intersecting a linear Function Examples). Answer student questions and comments.

15. Work example 15 (see attached file Sloping and Intersecting a linear Function Examples). Answer student questions and comments.

16. Work example 16 (see attached file Sloping and Intersecting a linear Function Examples). Answer student questions and comments.

17. Work example 17 (see attached file Sloping and Intersecting a linear Function Examples). Answer student questions and comments.

18. Work example 18 (see attached file Sloping and Intersecting a linear Function Examples). Answer student questions and comments.

19. Give students an example of slope and then discuss what is meant when the term slope is used (see # 19 on attached file Sloping and Intersecting a linear Function Examples). Answer student questions and comments.

20. Discuss the definition of slope from a graph and from a table (see # 20 on attached file Sloping and Intersecting a linear Function Examples). Answer student questions and comments.

21. Discuss the definition of slope (see # 21 on attached file Sloping and Intersecting a linear Function Examples). Answer student questions and comments.

22. Work example 22 (see attached file Sloping and Intersecting a linear Function Examples). Answer student questions and comments.

23. Work example 23 (see attached file Sloping and Intersecting a linear Function Examples). Answer student questions and comments.

24. Discuss with students how to graph when you only know one point and the slope (see # 24 on attached file Sloping and Intersecting a linear Function Examples). Answer student questions and comments.

25. Describe the four various ways slope can occur (see # 25 on attached file Sloping and Intersecting a linear Function Examples). Answer student questions and comments.

26. Graph 3 parallel lines on the same grid. Discuss their similarities and differences (see # 26 on attached file Sloping and Intersecting a linear Function Examples). Answer student questions and comments.

27. Discuss y-intercept of a graph (see # 27 on attached file Sloping and Intersecting a linear Function Examples). Answer student questions and comments.

28. Discuss x-intercept of a graph (see # 28 on attached file Sloping and Intersecting a linear Function Examples). Answer student questions and comments.

29. Work example 29 (see attached file Sloping and Intersecting a linear Function Examples). Answer student questions and comments.

30. Work example 22 (see attached file Sloping and Intersecting a linear Function Examples). Answer student questions and comments.

31. Distribute the Sloping and Intersecting a linear Function Worksheet (see attached file).

32. Distribute the Sloping and Intersecting a linear Function Checklist (see attached file). Describe what constitutes an “A,” “B,” “C,” “D,” and an “F” in the CHECKLIST.

33. The student will write their response on the worksheet.

34. The teacher will move from student to student observing the students work and lending assistance.

#### Assessments

Student worksheets will be taken up and scored according to “Sloping and Intersecting a linear Function Checklist”. These scores may be placed in the grade book.

#### Extensions

Using a geoboard as a model for the coordinate plane. Let the peg in the lower left-hand corner represent the origin. Have students make as many line segments with different nonnegative slopes as possible.