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

2-3 Translating Between Tables and Expressions Write an expression for the missing value in the table. Additional Example 1: Writing an Expression = 6 Spike’s Age = = 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.

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  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.

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 Value Guess 7nGuess 3n + 4 Check by substituting does not equal = 10. The expression 3n + 4 works for the entire sequence = 7, = 10, = 13, = 16 The expression for the sequence is 3n + 4.

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 Value Guess 7nGuess 5n + 2 Check by substituting does not equal = 12. The expression 5n + 2 works for the entire sequence = 7, = 12, = 17, = 22 The expression for the sequence is 5n + 2.

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 ) h 6 1 = 6, 6 ÷ 2 = = 12, 12 ÷ 2 = = 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

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 ) h 4 3 = 12, 12 ÷ 2 = = 16, 16 ÷ 2 = = 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