1. Tables and Functions
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2. VOCABULARY
A function is a rule that relates two quantities so that each input value corresponds exactly to one output value.

3. Example 1: Writing Equations from Function Tables
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 3 2 1 x

4. Example 2
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. 18 15 12 9 y 10 6 5 4 3 x ?

5. Example 3
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. 17 15 13 11 y 8 7 6 5 x ?

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

7. Example 4: Translating Words into Math
Write an equation for the function. Tell what each variable you use represents.
The height of a painting is 7 times its width.

8. Example 5
Write an equation for the function. Tell what each variable you use represents.
The height of a mirror is 4 times its width.

9. Example 6
Write an equation for the function. Tell what each variable you use represents.
A large pie costs $2 more than a small pie.

10. Example 7: Problem Solving Application
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.

11. Example 8
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.

12. Example 9: Finding Solutions of Equations with Two Variables
Use the given x-values to write solutions of the equation y = 4x + 2 as ordered pairs. x = 1, 2, 3, 4.

13. Example 10
Use the given x-values to write solutions of the equation y = 5x + 3 as ordered pairs. x = 2, 3, 4.

14. FYI
Check if an ordered pair is a solution of an equation by putting the x and y values into the equation to see if they make it a true statement.

15. Example 11: Checking Solutions of Equations with Two Variables
Determine whether the ordered pair is a solution to the given equation.
(3, 21); y = 7x

16. Example 12
Determine whether the ordered pair is a solution to the given equation.
(6, 4); y = 2x - 7

17. VOCABULARY
You can also graph the solutions of an equation on a coordinate plane. When you graph the ordered pairs of some functions, they form a straight line. The equations that express these functions are called linear equations.

18. Example 13: Reading Solutions on Graphs
Use the graph of the linear function to find the value of y for the given value of x.
x = 4 x y 4 2 -2 -4

19. Example 14
For each graph of a linear function, find the values of y for the values of x given below the graph.
x = 0 y 2 x 9 8 7 6 5 1 3 4 10

20. Example 15
For each graph of a linear function, find the values of y for the values of x given below the graph.
x = 4 y 2 x 9 8 7 6 5 1 3 4 10

21. Example 16: Graphing Linear Functions
Graph the function described by the equation. y = 3x+ 2

22. Example 17
Graph the function described by the equation. y = 8 - x