1. Relations as Ordered Pairs A light plane glides when the engine is turned off. Pilots use the saying “five for one”. This means that the plane will glide 5 m for every 1 m of altitude, 500 m for every 100m of altitude. Altitude (m) Glide Distance (m) 100500 200 600 1000 1500 2000 Ordered Pair – A pair of numbers, (x,y), that show the x- and y- coordinates of a point on a coordinate plane. Write an equation in the form d = __ x a to find the glide distance, d, from the altitude, a. d = 5 x a. Use this equation to find the glide distance for: a) 400m b) 1250m

2. Ordered Pairs This solution can be written as the ordered pair (3,4). The x- value comes first, then the y- value. A set of ordered pairs is known as a relation. A relation can be written as an equation, a table of values, or in words. The equation x + 1 = 4 has one variable, x. There is one solution, x = 3, that makes the equation true. There are two variables in the equation x + y = 7. There are many solutions, or values of the variables, that make the equation true. One solution is x = 3 and y = 4, because 3 + 4 = 7.

3. Ordered Pairs Example 1 Use the equation x + y = 4 a)Describe the relation in words – The sum of the x – and y- values is four. b) Complete the table of values for x = 3, 2, 1, 0, -1. x y 3 1 2 2 1 3 0 4 5 x + y = 4 3 + 1 = 4 2 + 2 = 4 1 + 3 = 4 0 + 4 = 4 -1 + 5 = 4 c) Write the ordered pairs The ordered pairs are (3,1), (2,2), (1,3), (0,4), (-1,5).

4. Ordered Pairs Example 2 Use the equation y = 2x + 3. a) Describe the relation in words. The value of y is two times the value of x, plus 3. b) Complete a table of values for x = 2, 1, 0, -1, -2. x y 2 7 1 5 0 3 1 -2 Y = 2x + 3 Y = 2(2) + 3 = 7 Y = 2(1) + 3 = 5 Y = 2(0) + 3 = 3 Y = 2(-1) + 3 = 1 Y = 2(-2) + 3 = -1 c) Write the ordered pairs. The ordered pairs are (2,7), (1,5), (0,3), (-1,1), and (- 2,-1).