Over Lesson 1–3 A.A B.B C.C D.D 5-Minute Check 1 A.Multiplicative Identity B.Additive Identity C.Associative Property of Addition D.Associative Property of Multiplication Name the property shown by the statement (4b)c = 4(bc). Name the property shown by the statement 4y + 0 = 4y. A.Multiplicative Identity B.Additive Identity C.Commutative Property of Addition D.Associative Property of Addition

Splash Screen

Then/Now You have already graphed numbers on number lines. (Previous Course) Use ordered pairs to locate points. Use graphs to represent relations.

Vocabulary coordinate system coordinate plane y-axis origin x-axis ordered pair x-coordinate y-coordinate graph relation domain range

What is the coordinate plane? It is two intersecting lines drawn to find locations These intersecting lines are the x-axis (horizontal axis) and the y-axis (vertical axis) These locations are called ordered pairs. An ordered pair is written as its x-value and its y- value or (x,y) Example: (3,4) means go 3 right and 4 up. The point (0,0) is referred to as the origin

Quadrants The intersecting lines break the coordinate plane into four Quadrants. These regions allow us to locate on a coordinate plane where certain points are located

I give you the Coordinate Plane (we need graph paper now) Y-axis X-axis Quadrant 1 (+,+) Quadrant 2 (-,+) Quadrant 3 (-,-) Quadrant 4 (+,-) Origin (0,0)

Example 1A Graph Ordered Pairs A. Graph the ordered pair (3, 4) on a coordinate plane. Step 1Start at the origin. Step 2Since the x-coordinate is 3, move 3 units to the right. Step 3Since the y-coordinate is 4, move 4 units up. Draw a dot. Answer:

Example 1B Graph Ordered Pairs B. Graph the ordered pair (0, 2) on a coordinate plane. Step 1Start at the origin. Step 2Since the x-coordinate is 0, you will not need to move to the right. Step 3Since the y-coordinate is 2, move 2 units up. Draw a dot. Answer:

A.A B.B C.C D.D Example 1A A. Graph the ordered pair (2, 5) on a coordinate plane. A.B. C.D.none of the above

A.A B.B C.C D.D Example 1B B. Graph the ordered pair (4, 0) on a coordinate plane. A.B. C.D.none of the above

Example 2A Identify Ordered Pairs Step 1Start at the origin. A. Write the ordered pair that names point G. Answer: The ordered pair for G is (1, 1). Step 2Move right on the x-axis to find the x-coordinate of point G, which is 1. Step 3Move up the y-axis to find the y-coordinate, which is 1.

Example 2B Identify Ordered Pairs B. Write the ordered pair that names point H. Step 1Start at the origin. Answer: The ordered pair for H is (4, 0). Step 2Move right on the x-axis to find the x-coordinate of point H, which is 4. Step 3Since the y-coordinate is zero, you will not need to move up.

A.A B.B C.C D.D Example 2A A.(2, 5) B.(3, 5) C.(2, 3) D.(3, 2) A. Write the ordered pair that names point A.

A.A B.B C.C D.D Example 2B A.(6, 6) B.(0, 6) C.(0, 0) D.(6, 0) B. Write the ordered pair that names point B.

Domain is the collection of all the x-values in a relation or a graph Range is the collection of all the y-values in a relation or a graph

Example 3 Relations as Tables Express the relation {(1, 4), (2, 2), (3, 0), (0, 2)} as a table. Then determine the domain and range. Answer: The domain is {0,1, 2, 3}. The range is {0, 2, 4}.

A.A B.B C.C D.D Example 3 Express the relation {(4, 1), (3, 2), (0, 1), (2, 3)} as a table. Then determine the domain and range. A.D = {1, 2, 3}, R = {0, 2, 3, 4} B.D = {0, 2, 3, 4}, R = {1, 2, 3} C.D = {2, 3, 4}, R = {1, 2, 3} D.D = {1, 2, 3}, R = {2, 3, 4}

Example 4A Relations as Graphs EARNINGS José earns $5 an hour doing yard work. A. Make a table of ordered pairs in which the x-coordinate represents the hours worked and the y-coordinate represents the amount of money José earns for 1, 2, 3, and 5 hours of work. Answer:

Example 4B Relations as Graphs EARNINGS José earns $5 an hour doing yard work. B. Graph the ordered pairs and describe the graph.

Example 4B Relations as Graphs Answer: The points appear to lie on a line.

End of the Lesson