I C A N U S E T A B L E S , E Q U A T I O N S , A N D G R A P H S T O D E S C R I B E R E L A T I O N S H I P S

1.9 PATTERNS, EQUATIONS, & GRAPHS

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= 4x?• 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 = 9x

• 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