1. 2-3 Translating Between Tables and Expressions Learn to write expressions for tables and sequences.

2. 2-3 Translating Between Tables and Expressions Write an expression for the missing value in the table. Additional Example 1: Writing an Expression 2 + 4 = 6 Spike’s Age 2 3 4 6 7 8 4 + 4 = 8 3 + 4 = 7 Rusty’s Age a a + 4 Rusty’s age is Spike’s age plus 4. a + 4 When Spike’s age is a, Rusty’s age is a + 4.

3. 2-3 Translating Between Tables and Expressions Write an expression for the missing value in the table. Check It Out: Example 1 1  7 = 7 Ty’s Age 1 2 3 7 14 21 3  7 = 21 2  7 = 14 Rich’s Age a a  7 Rich’s age is Ty’s age times 7. a  7 When Ty’s age is a, Rich’s age is a  7 or 7a.

4. 2-3 Translating Between Tables and Expressions Write an expression for the sequence in the table. Additional Example 2: Writing an Expression for a Sequence Look for a relationship between the positions and the values of the terms in the sequence. Use guess and check. Position1234n Value7101316 Guess 7nGuess 3n + 4 Check by substituting 2. 7 2 does not equal 10.3 2 + 4 = 10. The expression 3n + 4 works for the entire sequence. 3 1 + 4 = 7, 3 2 + 4 = 10, 3 3 + 4 = 13, 3 4 + 4 = 16 The expression for the sequence is 3n + 4.

5. 2-3 Translating Between Tables and Expressions Write an expression for the sequence in the table. Check It Out: Example 2 Look for a relationship between the positions and the values of the terms in the sequence. Use guess and check. Position1234n Value7121722 Guess 7nGuess 5n + 2 Check by substituting 2. 7 2 does not equal 12.5 2 + 2 = 12. The expression 5n + 2 works for the entire sequence. 5 1 + 2 = 7, 5 2 + 2 = 12, 5 3 + 2 = 17, 5 4 + 2 = 22 The expression for the sequence is 5n + 2.

6. 2-3 Translating Between Tables and Expressions Additional Example 3: Writing an Expressions for the Area of a Figure A triangle has a base of 6 inches. The table shows the area of the triangle for different heights. Write an expression that can be used to find the area of the triangle when its height is h inches. Base (in.)Height (in.)Area (in 2 ) 613 626 6412 6h 6 1 = 6, 6 ÷ 2 = 3 6 2 = 12, 12 ÷ 2 = 6 6 4 = 18, 18 ÷ 2 = 9 In each row of the table, the area is half the product of the base and the height. The expression is or 3h. 6h6h 2 __ 3h3h

7. 2-3 Translating Between Tables and Expressions Check It Out: Example 3 A triangle has a base of 4 inches. The table shows the area of the triangle for different heights. Write an expression that can be used to find the area of the triangle when its height is h inches. Base (in.)Height (in.)Area (in 2 ) 436 448 4510 4h 4 3 = 12, 12 ÷ 2 = 6 4 4 = 16, 16 ÷ 2 = 8 4 5 = 20, 20 ÷ 2 = 10 In each row of the table, the area is half the product of the base and the height. The expression is or 2h. 4h4h 2 __ 2h2h