Algebra 5.1

1. Algebra 5.1 Identifying Linear Functions

2. Learning Targets Language Goal • Students will be able to identify linear functions and linear equations. Math Goal • Students will be able to graph linear functions that represent real-world situations and give their domain and range. Essential Questions • What is a real-world situation that represents a linear function?

3. Warm-up

4. Vocabulary • Linear Function: • Linear Equation: A function whose graph forms a straight line. Any equation that can be written in standard form.

5. Identifying Linear Functions • There are 3 ways to identify. • By its Graph • By using Ordered Pairs • By its Equation

6. Identifying by its Graph • Your first step is to identify if the graph is a function • Remember a function is when one domain value is paired with exactly one range value. • You can do the vertical line test! • If the graph is a function, tell whether it is linear. • A linear graph means that it forms a straight line.

7. Identifying by its Graph • Identify whether each graph represents a function. Explain. If the graph does represent a function, is the function linear? Function? __________ If yes, Linear? _______ Function? __________ If yes, Linear? _______ Function? __________ If yes, Linear? _______ Function? __________ If yes, Linear? _______

8. Example 1: Your Turn! Function? __________ If yes, Linear? _______ Function? __________ If yes, Linear? _______ Function? __________ If yes, Linear? _______

9. Identifying by using Ordered Pairs • It might help to write all ordered pairs into a table. • For example: {(2, 5), (4, 8), (6, 11)} • In a linear function, a constant change in x corresponds to a constant change in y. ***Remember both x and y need to have a constant change in values. It does not have to be the same constant! +2 +3 +2 +3

10. Identifying by using Ordered Pairs Example Non Example +1 - 3 - 3 +1 +1 - 1 +1 - 3 +1 +1 +1 - 3 +1 - 3 +3 +1 Constant change in x and y Linear Function Constant change in x and but not y Not a linear function

11. Identifying by using Ordered Pairs • Tell whether each set of ordered pairs satisfies a linear function. Explain. A. {(2, 4). (5, 3), (8, 2), (11, 1)} B.{(-10, 10), (-5, 4), (0 2), (5, 0)}

12. Example 2: Your Turn! • Tell whether each set of ordered pairs satisfies a linear function. Explain. C. {(3, 5). (5, 4), (7, 3), (9, 2), (11, 1)} D.{(0, -3), (4, 0), (8, 3), (12, 6), (16, 9)} E. {(-4, 13), (-2, 1), (0, -3), (2, 1), (4, 13)}

13. Identifying by using the Equation • If an equation can be written in standard form, then it is a linear equation. • What is standard form? Ax + By = C where A, B, and C are real numbers and A and B are not both 0.

14. Identifying by using the Equation • Notice that when a linear equation is written in standard form… • x and y both have exponents of 1 • x and y are not multiplied together • x and y do not appear in denominators, exponents or radical signs.

15. Identifying by using the Equation Standard Form: Ax + By = C

16. Practice Re-Writing in Standard Form 1. 2. 3.

17. Identifying by using an Equation • Tell whether each function is linear. 1. 2. 3. y = 12

18. Identifying by using an Equation • Tell whether each function is linear. If yes graph the function. A. B. y = 12 C. D.

19. Example 3: Your turn • Tell whether each function is linear. If yes graph the function. A. B. C. D.

20. Review

21. Word Application • Sue rents a manicure station in a salon and pays the salon owner $5.50 for each manicure she gives. The amount she pays each day is given by f(x) = 5.50x, where x is the number of manicures. Graph the function and give its domain and range.

22. Word Application • The relationship between human years and dog years is given by the function y = 7x, where x is the number of human years. Graph this function and give its domain and range.