Warmup Give an example of an ordered pair

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

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 Month Jan Feb March April May Number 22 29 43 76 41 If we think of January as month 1, how could we write the data in the table as ordered pairs?

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 ( -2 , 3 ) (- 1 , - 1) ( 0, 2) (1 , 3) Name the domain of the relation above _____________ Name the range of the relation above ______________ Graph

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

Warmup State the domain and range of the relation below. (Use braces) (2, 1) (-5, 4) (-8, 0) (1/2, 4)

Year 1900 1920 1940 1960 1980 2000 15. 5 21. 6 25. 4 36. 1 41. 7 46. 6 Number of Students (millions) 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?

6. 2: Equations as Relations What is the solution of the equation 2 x + 3 = 7 ? What is the solution of the equation 2 x + y = 4?

What is the solution of the equation How many solutions are there? Can you name them? 2 x + y = 4?

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

“plug and chug” Ex 1) Which of the ordered pairs are solutions of Show work and answer yes / no. ( 0, 2) ( 6 , -2 ) 2 x + 3 y = 6 (3, -1)

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

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

On your own: 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. 2 x+y=7

� � � 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___

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

Everyone to the board! Write your birthday (month and year) Work with a partner to come up with an equation that has at least 2 of these solutions

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.