Five-Minute Check (over Lesson 1–5)CCSSThen/NowNew VocabularyExample 1: Representations of a RelationExample 2: Real-World Example: Independent and

Dependent VariablesExample 3: Analyze Graphs

Over Lesson 1–5

A. 7

B. 9

C. 13

D. 16

What is the solution of 5b – 11 = 34 given the replacement set {7, 9, 13, 16, 22}?

Over Lesson 1–5

A.

B.

C.

D.

Over Lesson 1–5

A. 6

B. 4

C. 0

D. –1

Solve (6 – 42 ÷ 7) + k = 4.

Over Lesson 1–5

A. 15

B. 10

C. 9

D. 5

Solve (3 + 42 – 9)m = 90.

Over Lesson 1–5

A. 3.8

B. 3.6

C. 3.4

D. 3.0

Solve 8a – (15 – 3.2) = a + (52 – 13).

Over Lesson 1–5

A. 896

B. 104

C. 42

D. 24

• Pg. 40 – 46• Obj: Learn how to represent relations and

interpret graphs of relations.• Content Standards: A.REI.10 and F.IF.1

• Why?– The deeper in the ocean you are, the greater

pressure is on your body. This is because there is more water over you. The force of gravity pulls the water weight down creating a greater pressure. The equation that relates the total pressure of the water to the depth is P=rgh.

• What happens to the pressure on your body as you dive deeper into the ocean?

• Does the pressure depend on the depth or does the depth depend on the pressure

• Which variable do you think is the dependent variable? Independent variable?

You solved equations with one or two variables.

• Represent relations.

• Interpret graphs of relations.

• Coordinate System – formed by the intersection of two number lines

• y-axis – the vertical axis• x-axis – the horizontal axis• Origin – the point where the axes meet (0,0)• Ordered Pair – a set of numbers, or coordinates,

written in the form (x,y)• x-coordinate – represents the horizontal

placement of the point• y-coordinate – represents the vertical placement

of the point

• Relation – a set of ordered pairs• Mapping – illustrates how each element of the

domain is paired with an element in the range• Domain – the set of the first numbers of the

ordered pairs• Range – the set of the second numbers of the

ordered pairs• Independent Variable – the value of the variable

that determines the output• Dependent Variable – the variable with a value that

is dependent on the value of the independent variable

Representations of a Relation

A. Express the relation {(4, 3), (–2, –1), (2, –4), (0, –4)} as a table, a graph, and a mapping. Table List the x-coordinates in the first column and the corresponding y-coordinates in the second column.

Representations of a Relation

Graph Graph each ordered pair on a coordinate plane.

Representations of a Relation

Mapping List the x-values in the domain and the y-values in the range. Draw an arrow from the x-value to the corresponding y-value.

4

–2

2

0

3

–1

–4

Domain Range

Representations of a Relation

B. Determine the domain and range for the relation {(4, 3), (–2, –1), (2, –4), (0, –4)}.

Answer: The domain for this relation is {4, –2, 2, 0}. The range is {3, –1, –4}.

A. Express the relation {(3, –2), (4, 6), (5, 2), (–1, 3)} as a mapping.

A. C.

B. D.

B. Determine the domain and range of the relation {(3, –2), (4, 6), (5, 2), (–1, 3)}.

A. D = {–1, 3, 4, 5}; R = {–2, 2, 3, 6}

B. D = {–2, 2, 3, 6}; R = {–1, 3, 4, 5}

C. D = {–1, 3}; R = {–2, 2}

D. D = {4}; R = {4}

Independent and Dependent Variables

A. CLIMATE In warm climates, the average amount of electricity used rises as the daily average temperature increases, and falls as the daily average temperature decreases. Identify the independent and the dependent variables for this function.

Answer: Temperature is the independent variable, as it is unaffected by the amount of electricity used. Electricity usage is the dependent variable, as it is affected by the temperature.

Independent and Dependent Variables

B. The number of calories you burn increases as the number of minutes that you walk increases. Identify the independent and the dependent variables for this function.

Answer: The time is the independent variable. The number of calories burned is the dependent variable, as it is affected by the time.

A. The number of new members is the independent variable. The dues is the dependent variable.

B. Membership dues is the independent variable. The number of new members is the dependent variable.

C. x is the independent variable. y is the dependent variable.

D. Both variables are independent.

A. In a particular club, as membership dues increase, the number of new members decreases. Identify the independent and dependent variable in this function.

A. The length of the side is independent, and the the area of the square is dependent.

B. The area is independent, and the side length is dependent.

C. Both variables are independent.

D. Both variables are dependent.

B. The area of a square increases as the length of a side increases. Identify the independent and dependent variable in this function.

Analyze Graphs

The graph represents the temperature in Ms. Ling’s classroom on a winter school day. Describe what is happening in the graph.

Sample answer: The temperature increases after the heat is turned on. Then the temperature fluctuates up and down because of the thermostat. Finally, the temperature drops when the heat is turned off.

A. Macy is doing bobs.B. Macy’s speed increases as she

crosses the length of the pool, but then decreases to zero when she turns around at the end of each lap.

C. Macy is swimming at a constant speed.

D. Macy’s speed continues to decrease.

The graph represents Macy’s speed as she swims laps in a pool. Describe what is happening in the graph.