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Understanding Linear Functions Through Real-World Examples

This lesson on linear functions features practical examples, including Chuck's commute to work and a photography studio's pricing. Students will learn to calculate distance over time and analyze the relationship between independent and dependent variables. The task involves completing tables, graphing data, writing equations, and identifying domain and range. By the end, learners will grasp essential concepts related to linear functions, equipping them with skills to handle real-world linear scenarios effectively.

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Understanding Linear Functions Through Real-World Examples

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  1. 8-1: Linear Functions Mr. Gallo

  2. Example 1 – Chuck is going to work after school today. If school is 5 miles north of his home and he travels to his job at a constant rate of speed of 0.5 miles per minute in a northern direction, how far from his home will he be in 5 minutes? Complete the table and graph the data on the chart below. Write the equation you would use to represent this situation: ________________

  3. Linear Functions linear • An equation whose graph is a line is called a __________ function. • Using the graph created in Example 1 the distance is a _______________ of time because how far you travel is dependent on the time . • Distance is the ________________ variable because it depends on how long you are traveling to determine the distance traveled. • Time is the ______________ variable because it determines the final answer. function dependent independent

  4. Domain and Range • Using the information from Example 1 what is the set of values used for t? _________________ • The set of the first coordinates in an ordered pair is called the ___________of the function. • List the set of coordinates of the second variable in the ordered pairs: ________________________ • These represent the values for D (distance) or the ___________ of the function. domain range

  5. Example 2- A photography studio charges $5 per sitting and an additional $3 for each print ordered. Represent the number of prints ordered by pand the cost of the prints by c. Write a function to express the cost of the prints in terms of p. Graph the function for orders of 5 to 25 prints. What is the independent variable? __________________ What is the dependent variable? __________________ What is the domain? __________________ What is the range? __________________

  6. Graph the function for orders of 5 to 25 prints:

  7. Example 3– Find the values for y by substituting -2, -1, 0, 1, and 2 in for x. Make a table and graph your results.

  8. Homework: WS 8.1 Day 2

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