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# Slopes of Linear Functions

Lesson 8 of 13

## Objective: SWBAT find slopes of linear functions using different given information and find linear functions and data points to fit certain requirements.

## Big Idea: Given the slope of a line and a point on the line, what can you figure out? How can you find other points on the line?

*70 minutes*

#### Warm-Up

*30 min*

Students should be experts on the first problem, which is a summative review of last week's work. The layout helps students make connections between the different representations. As they work on these problems you can repeatedly ask them to explain how the key properties of linear functions show up in these different representations. The emphasis of this problem should be on student’s justifications for their work (**MP3**).

The second problem provides the opportunity to talk about the concept of slope more abstractly rather than quantitatively (**MP2**). The numbers that students choose don’t matter as much as the relationship between the linear equations that the students write.

The third problem provides students with the chance to understand a new type of problem. First, they need to figure out what it is asking (**MP1**). As it is the beginning of the year, they may be waiting for you to tell them how to solve this problem. This is an important time to require them to engage in the sense-making process. How does this work? Provide them with support, without actually answering any of their questions. See the MP1 Questions and Coaching document for specific ways of speaking to help make this happen.

Often when we want students to make sense of problems, we tell them, “Try again,” or “Ask your partner.” While this might be good advice, it often makes students feel that we are brushing them off, or that we don’t want to help them. The alternative sentences in the document help you show students that you care about their learning and are willing to invest time to help them, but that you aren’t going to actually show them how to do the problem.

*expand content*

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- UNIT 1: Linear and Nonlinear Functions
- UNIT 2: Piecewise Functions
- UNIT 3: Absolute Value Functions and More Piecewise Functions
- UNIT 4: Introduction to Quadratic Functions through Applications
- UNIT 5: More Abstract Work with Quadratic Functions
- UNIT 6: Rational Functions
- UNIT 7: Polynomial Functions
- UNIT 8: Exponential Functions
- UNIT 9: Ferris Wheels
- UNIT 10: Circles
- UNIT 11: Radical Functions
- UNIT 12: Cubic Functions

- LESSON 1: Patchwork Tile Patterns
- LESSON 2: Investigating Linear and Nonlinear Tile Patterns
- LESSON 3: More Tile Patterns
- LESSON 4: Constant Speeds and Linear Functions
- LESSON 5: Linear and Nonlinear Functions
- LESSON 6: Real World Relationships
- LESSON 7: Sketching Graphs for Real-World Situations
- LESSON 8: Slopes of Linear Functions
- LESSON 9: Different Forms of Linear Equations
- LESSON 10: Linear Function Designs
- LESSON 11: Verbal Descriptions of Linear and Nonlinear Functions
- LESSON 12: Linear and Nonlinear Function Review and Portfolio
- LESSON 13: Linear and Nonlinear Functions Summative Assessment