The document provides examples and explanations of writing equations to describe functions from tables, words, and real-world scenarios. It includes examples of writing equations for linear functions given tables of x and y values, translating word problems into mathematical equations, and using data about tickets sold and money received to write an equation for that function. Practice problems are provided to write equations for new functions based on the examples and explanations given.

1. Warm Up Lesson Presentation Problem of the Day Lesson Quizzes

2. Warm Up Evaluate each expression for the given value of the variable. 1. 4 x – 1 for x = 2 2. 7 y + 3 for y = 5 3. 8 x + 2 for x = 6 4. 8 y – 3 for y = 2 7 38 50 13

3. Problem of the Day These are rits : 24042, 383, and 4994. These are not rits : 39239, 28, and 5505. Which of these are rits : 39883, 4040, and 101? Why? 101 is a rit because it is the same forward and backward

4. MA.6.A.3.6 Construct and analyze tables…and equations to describe linear functions…using both common language and algebraic notation. Also MA.6.A.3.2 Sunshine State Standards

5. Vocabulary function input output

6. A function is a rule that relates two quantities so that each input value corresponds exactly to one output value.

7. Additional Example 1: Writing Equations from Function Tables y is 3 times x plus 4. y = 3 x + 4 y = 3(10) + 4 y = 30 + 4 = 34 Write an equation for a function that gives the values in the table. Use the equation to find the value of y for the indicated value of x . 16 13 10 7 4 y 10 4 3 2 1 0 x Compare x and y to find a pattern. Use the pattern to write an equation. Substitute 10 for x. Use your rule to find y when x = 10.

8. Check It Out: Example 1A Write an equation for a function that gives the values in the table. Use the equation to find the value of y for the indicated value of x . ? y is 3 times x y = 3x y = 3(10) y = 30 18 15 12 9 y 10 6 5 4 3 x

9. Check It Out: Example 1B Write an equation for a function that gives the values in the table. Use the equation to find the value of y for the indicated value of x . ? y is 1 more than 2 times x y = 2x + 1 y = 2(15) + 1 = 30 + 1 = 31 17 15 13 11 y 15 8 7 6 5 x

10. You can write equations for functions that are described in words.

11. Additional Example 2: Translating Words into Math The height of a painting is 7 times its width. h = height of painting h = 7 w Write an equation for the function. Tell what each variable you use represents. w = width of painting Choose variables for the equation. Write an equation.

12. Check It Out: Example 2A The height of a mirror is 4 times its width. Write an equation for the function. Tell what each variable you use represents. h = height of mirror h = 4 w w = width of mirror

13. Check It Out: Example 2B A large pie costs $2 more than a small pie. Write an equation for the function. Tell what each variable you use represents. ℓ = large pie’s cost s = small pie’s cost ℓ = 2 + s

14. The school choir tracked the number of tickets sold and the total amount of money received. They sold each ticket for the same price. They received $80 for 20 tickets, $88 for 22 tickets, and $108 for 27 tickets. Write an equation for the function. The answer will be an equation that describes the relationship between the number of tickets sold and the money received. Additional Example 3: Problem Solving Application 1 Understand the Problem

15. You can make a table to display the data. Let t be the number of tickets. Let m be the amount of money received. m is equal to 4 times t . m = 4 t 2 Make a Plan Solve 3 108 88 80 m 27 22 20 t Compare t and m. Write an equation.

16. Substitute the t and m values in the table to check that they are solutions of the equation m = 4 t . m = 4 t (20, 80) ‏ m = 4 t (22, 88) ‏ m = 4 t (27, 108) ‏ Look Back 4 80 = 4 • 20 ? 80 = 80 ? 88 = 4 • 22 ? 88 = 88 ? 108 = 4 • 27 ? 108 = 108 ?

17. Check It Out: Example 3 The school band tracked the number of tickets sold and the total amount of money received. They sold each ticket for the same price. They received $60 for 20 tickets, $66 for 22 tickets, and $81 for 27 tickets. Write an equation for the function.

18. m = 3 t Let t be the number of tickets. Let m be the amount of money received. Check It Out: Example 3 continued 81 66 60 m 27 22 20 t

19. Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

20. Lesson Quiz 1. Write an equation for a function that gives the values in the table below. Use the equation to find the value for y for the indicated value of x . 2. Write an equation for the function. Tell what each variable you use represents. The height of a round can is 2 times its radius. h = 2 r , where h is the height and r is the radius y = 3 x ; 21 15 9 3 0 y 7 5 3 1 0 x

21. 1. Identify an equation for a function that gives the values in the table below. Then, use the equation to find the value for y for the indicated value of x . A. y = 4 x + 8; 21 B. y = 7 x – 7; 21 C. y = 4 x + 8; 28 D. y = 7 x – 7; 28 Lesson Quiz for Student Response Systems

22. 2. Identify an equation for the function. Tell what each variable you use represents. The width of a swimming pool is twice its depth. A. w = 2 d , where d is the width and w is the depth B. , where w is the width and d is the depth C. w = 2 d , where w is the width and d is the depth D. , where d is the width and w is the depth Lesson Quiz for Student Response Systems