give an example of an ordered pair (take a guess if you don’t know)

Give an example of an ordered pair (take a guess if you don’t know).

Warmup

In real life we study patterns and trends to try and predict or prevent what might happen in the future. The table below shows the estimated number of sea turtles found stranded on the Texas Gulf Coast over several months in a recent year.

Sea Turtles Stranded If we think of January as

month 1, how could we write the data in the table as ordered pairs?

Month Number Jan 22 Feb 29 March 43 April 76May 41

Now use the ordered pairs to graph the data below. What do you notice? Explain.

The first coordinate in an ordered pair is called the x-coordinate

The second coordinate in an ordered pair is called the y-coordinate.

  A set of ordered pairs, such as the one above for the

sea turtles, is a relation.

The set of all x-coordinates is called the domain of the relation.

The set of all y-coordinates is called the range of the relation.

A relation can be shown in several ways:  Ordered Pairs Table Graph

( -2 , 3 ) (- 1 ,- 1) ( 0 , 2 ) ( 1 , 3 )

Name the domain of the relation above __________________________ Name the range of the relation above

____________________________

Ex 1) Express the relation { ( -2,4) , ( 2, -2), ( 3,3), ( 4 , 2 ), (3,-1)} as a table and as a

graph. Then determine the domain and range.

Ex 2) Express the relation shown on the graph as a set of ordered pairs and in a table. Then determine the domain and range.

Table Ordered Pairs Domain & Range

State the domain and range of the relation below. (Use braces)

(2,1)(-5,4)(-8,0)(1/2,4)

Warmup

Year 1900 1920 1940 1960 1980 2000

Number of Students (millions)

15.5 21.6 25.4 36.1 41.7 46.6

A.) Determine the domain and range of the relation. Domain: Range:

B. Graph the relation. Be sure to label the x and y-axis.

C.During which time period was there the greatest increase in the number of students enrolled in public schools?

What is the solution of the equation 2 x + 3 = 7 ?

What is the solution of the equation 2 x + y = 4 ?

6.2: Equations as Relations

What is the solution of the equation 2 x + y = 4 ?

 How many solutions are there?  Can you name them?

Conclusion: If your equation has 2 variables, the solutions will be _____________________ that make the equation true.

Ex 1) Which of the ordered pairs are solutions of 2 x + 3 y = 6

Show work and answer yes / no.  ( 0 , 2 ) ( 3 , - 1 )  ( 6 , -2 )

“plug and chug”

Ex 2 ) Which of the ordered pairs are solutions of y = 3 x – 4   ( 1 , - 2 ) ( -2 , - 10 )    

1( , 6)3

4 1( , 5 )9 3

Create an equation using x and y that has a solution of (3,1) and you cannot use x+y=4

Warmup

Come up with an equation that uses x and y and has a solution (1,4)

Ex. x+y=5

Now come up with an equation that uses multiplication and has solution (2,3)

Ex. 2x+y=7

On your own:

Ex 3) Solve y = 2 x - 1 if the domain is { -2 , -1 , 0 , 1 , 2 }. Then graph your solutions.

What do you notice?  x y___

Ex 4 ) Solve 4 x + 2 y = 8 if the domain is { -2 , -1 , 0 , 1 , 2 } Then graph your solutions.

x y___

Do on white boards

Write your birthday (month and year)

Work with a partner to come up with an equation that has at least 2 of these solutions

Everyone to the board!

Any equation that graphs a line is called a ______________________ equation.

  Sometimes it is in standard form:

_________________________.  Sometimes it is solved for y which makes it

easier to graph.