Exploring Linear Functions_ Rate of Change & Initial Value.pptx

Understanding what is Rate of Change using Linear Function

1. Exploring Linear Functions: Rate of Change & Initial Value How can we analyze and build linear functions in math—and in real life? Melvin Flores

2. Look at the growth chart. Which statement best describes the change in the plant’s height each day? A) The plant grows by the same amount each day. B) The plant grows faster each day. C) The plant grows slower every day. Write the letter you choose and explain your thinking in one sentence. Bell Ringer: Spot the Pattern!

3. Self Reflection: Why Did You Choose That? Reflect on your bell ringer answer. What clues helped you decide which answer was correct? Write 2-3 sentences about your thinking!

4. A linear function is a rule that describes a steady (constant) rate of change between two things. When you graph it, the result is a straight line! Every linear function has: - A starting value (called the y-intercept) - A rate of change (called the slope) What Is a Linear Function?

5. Real-World Example: Lemonade Stand Imagine you earn $2 for every cup of lemonade you sell. If you start the day with $5 in your cash box, what linear function shows how much money you have after selling x cups? • Starting Value (y-intercept): $5 • Rate of Change (slope): $2 per cup

6. The equation for a linear function looks like this: y = mx + b Where... • y = output • m = rate of change (slope) • x = input • b = starting value (y-intercept) The Linear Function Equation How do we write it?

7. Let’s watch a short video showing how to find the rate of change and the starting value (y-intercept) in everyday situations! (Teacher: Insert video link here or show a quick demo!) Let’s Watch & Learn!

8. Check for Understanding: Practice Problem A runner jogs 3 laps every 5 minutes. She starts at 0 laps. Write a linear function for L, the number of laps after t minutes. What do the slope and y-intercept mean in this situation?

9. Look at this temperature graph. The temperature starts at 15°C and rises 2°C each hour. Let's write the equation: T = 2h + 15 What does 2 mean? What does 15 mean? I Do: Analyzing a Picture

10. Here's a table showing the number of books read each month: Month 0: 3 books Month 1: 6 books Month 2: 9 books Together: What is the rate of change? What is the starting value? Let's write the linear function as a class. We Do: Finding Slope and Intercept Together Let’s work through a table!

11. Check for Understanding: Quick Quiz Which equation represents a starting value of 10 and an increase of 4 each time? A) y = 10x + 4 B) y = 4x + 10 C) y = x + 14 Circle your choice and explain what the numbers mean.

12. Individually, solve the following: 1. Write a linear function for: A car that starts with 6 gallons of gas and uses 1 gallon every 20 miles. 2. What do the numbers represent in your equation? Try a similar one from your worksheet! You Do: Your Turn!

13. Fun Fact: Linear Functions are Everywhere! Linear functions are used by architects, car engineers, and meteorologists every day! From designing ramps to predicting temperatures, these simple equations help us understand—and plan—our world!

14. What is one new thing you learned about linear functions? How can you use this in real life? Write a quick note to yourself about how you feel about finding rates of change and starting values. Self-Reflection: What Did You Learn? Think about today’s activities

15. Before you leave: 1. Turn in your independent work. 2. Write a real-life example of a linear function you might see or use. Homework: Find a situation at home that could be modeled with a linear function, and write its equation. Be ready to share! Exit Ticket & Next Steps Let’s wrap up and get ready for next time!