Title: Lesson 8-2
Author: Kathy Halverson
Last saved by: Glencoe Mathematics
Company: Halverson Household

Lesson 7-2

Example 1	Use a Table of Ordered Pairs
Find four solutions of y = 3x + 2
x | y = 3x + 2 | y | (x, y)
0 | y = 3(0) + 2 | 2 | (0, 2)
1 | y = 3(1) + 2 | 5 | (1, 5)
2 | y = 3(2) + 2 | 8 | (2, 8)
3 | y = 3(3) + 2 | 11 | (3, 11)

Choose four values for x.  Then substitute each value into the equation and solve for y.

Four solutions are (0, 2), (1, 5), (2, 8), and (3, 11).

Real-World EXAMPLE 
Example 2	Solve an Equation for y
CLOTHING   A clothing store has all shirts on sale for $10 and pants for $20.  Find four solutions of 10x + 20y = 100 in terms of the numbers of shirts x and pants y McKenzie can buy with $100.  Explain each solution.

First, rewrite the equation by solving for y.

          10x + 20y	= 100		Write the equation.
 10x + 20y – 10x	= 100 – 10x		Subtract 10x from each side.
                    20y	= 100 – 10x 		Simplify.
                        y 	=  − 	Divide each side by ten.
                        y 	= 5 – 		Simplify.
x | y = 5 − | y | (x, y)
0 | y = 5 – (0) | 5 | (0, 5)
2 | y = 5 – (2) | 4 | (2, 4)
4 | y = 5 – (4) | 3 | (4, 3)
9 | y = 5 – (9) | 1 |
Choose four x values and substitute them into y = 5 − .     
(0, 5)	→     She can buy 0 shirts and 5 pants.
(2, 4)  	→     She can buy 2 shirts and 4 pants.
(4, 3) 	→     She can buy 4 shirts and 3 pants.
	→     This solution does not make sense because she cannot buy half a pair of pants.

Example 3	Graph a Linear Equation
Graph y = -x + 3 by plotting ordered pairs.
x | y = -x + 3 | y | (x, y)
-1 | y = -(-1) + 3 | 4 | (-1, 4)
0 | y = -(0) + 3 | 3 | (0, 3)
1 | y = -(1) + 3 | 2 | (1, 2)
2 | y = -(2) + 3 | 1 | (2, 1)

First, find ordered pair solutions.  Four 
solutions are (-1, 4), (0, 3), (1, 2), and (2, 1).  

Plot these ordered pairs and draw a line through them.  Note that the ordered pair for any point on this line is a solution of y = -x + 3.  The line is a complete graph of the function.

CHECK    It appears from the graph that (4, -1) is also a solution.  Check this by substitution.
  y = -x + 3		Write the equation.
-1  –(4) + 3		Replace x with 4 and y with –1.
-1 = -1  ✓		Simplify.