1 9 PATTERNS EQUATIONS GRAPHS I CAN USE

1. 9 PATTERNS, EQUATIONS, & GRAPHS I CAN USE TABLES, EQUATIONS, AND GRAPHS TO DESCRIBE RELATIONSHIPS

EQUATIONS WITH TWO VARIABLES • A solution of an equation with two variables x and y is the ordered pair (x, y). • The ordered pair is only a solution if it makes the equation true. • Ex: is (3, 10) a solution to the equation y= 4 x? • NO

DIFFERENT REPRESENTATIONS • Both Carrie and her sister Kim were born on October 25, but Kim was born 2 years before Carrie. • What are three different ways to represent the relationship between Kim’s age and Carrie’s age?

EQUATION • We know that Kim is 2 years older than Carrie. • How can we write an equation to show this relationship? • y=x+2 • y = Kim’s age • x = Carrie’s age • What would the equation be if x = Kim’s age and y=Carrie’s age? • y=x– 2

TABLE Carrie’s and Kim’s ages (years) Carrie 1 2 3 4 5 6 7 8 9 10 Kim 3 4 5 6 7 8 9 10 11 12

GRAPH

EXTENDING A PATTERN The table shows the relationship between the number of blue tiles and the total number of tiles. What is the total number of tiles in a figure with 8 blue tiles?

USING A GRAPH

USING AN EQUATION • Recognize the pattern in the table. • As x increases by 1, y increases by 9. • y = 9 x • Since x is the number of blue tiles, substitute 8 for x • y = 9(8) • y = 72 tiles

TRY IT! • In the same figure, create a table showing the relationship between the number of orange tiles and the total number of tiles. • Then, find how many total tiles will be in the figure if there are 28 orange tiles. • Hint: use a graph or an equation.

ASSIGNMENT • ODDS ONLY • P. 64 #9 -17, 21 -31