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Exploring Linear Functions: Graphs, Equations, and Slope Analysis

In this lesson, we dive into the fundamentals of linear functions, examining their properties through graphing, intercepts, and equations. Students will learn to identify linear functions both visually and numerically, understanding the relationship between changes in x and y. We will cover the different types of slopes—zero, positive, negative, and undefined—and what they signify. Additionally, exercises will involve finding slopes, evaluating functions, and understanding domain and range, ensuring a comprehensive grasp of linear functions.

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Exploring Linear Functions: Graphs, Equations, and Slope Analysis

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  1. Friday, October 4th Please Complete Warm Up Warm-Up September 27th Find Slope (-5, -1) (-4, 7) Find f(7) if f(x)=3x²+6x-10

  2. Homework Answers Think, Pair, share

  3. Identifying a Linear Function by Its Graph

  4. Identifying a Linear Function by it’s Table In a linear function, a _________ change in x corresponds to a ___________ change in y.

  5. Do you Remember? What should you NOT find in a linear Equation? 1. 2. 3. 4. 5.

  6. Finding Intercepts in an equation “__________up Method” 4x – 2y=14

  7. Different Slopes zero Positive Undefined Negative

  8. Slope Horizontal vs. Vertical Horizontal: 0Verical: Undefined

  9. EquationsHorizontal vs. Vertical Horizontal: y=no xVerical: x=no y

  10. Slope ALWAYS

  11. DOMAIN AND RANGE Graph has endpoints

  12. DOMAIN AND RANGE Graph doesn’t have endpoints

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