A6 APPENDIX Review Evaluating an Algebraic Expression Evaluate each expression if x 3 = and y 1. = − (a) x y3 + (b) xy 5 (c) y x 3 2 2 − (d) x y 4− + Solution EXAMPLE 7 (a) Substitute 3 for x and 1− for y in the expression x y3 . + x y3 3 3 1 3 3 0 ( ) ( ) + = + − = + − = ↑ = =− x y 3, 1 DEFINITION Distance Between Two Points If P and Q are two points on the real number line with coordinates a and b , respectively, the distance between P and Q , denoted by d P Q , ( ) , is d P Q b a , ( ) = − Since b a a b , − = − it follows that d P Q d Q P , , . ( ) ( ) = Figure 11 -5 7 P R Q 0 1 2 3 4 5 6 -1 -2 -3 -4 d(P, Q) = ƒ 7 - (-5) ƒ = 12 d(Q, R) = ƒ -3 - 7 ƒ = 10 Finding Distance on a Number Line Let P , Q , and R be points on the real number line with coordinates 5, 7, − and 3, − respectively. Find the distance (a) between P and Q (b) between Q and R Solution EXAMPLE 6 See Figure 11. (a) d P Q , 7 5 12 12 ( ) ( ) = − − = = (b) d Q R , 3 7 10 10 ( ) = − − = − = Now Work problem 49 4 Evaluate Algebraic Expressions Remember, in algebra we use letters such as x , y , a , b , and c to represent numbers. If a letter used is to represent any number from a given set of numbers, it is called a variable . A constant is either a fixed number, such as 5 or 3, or a letter that represents a fixed (possibly unspecified) number. Constants and variables are combined using the operations of addition, subtraction, multiplication, and division to form algebraic expressions . Examples of algebraic expressions include x t x y 3 3 1 7 2 + − − To evaluate an algebraic expression, substitute a numerical value for each variable.
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