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Five-Minute Check (over Lesson 1–5) Then/Now New Vocabulary Example 1: Representations of a Relation Example 2: Real-World Example: Independent and Dependent Variables Example 3: Analyze Graphs Lesson Menu

What is the solution of 5b – 11 = 34 given the replacement set {7, 9, 13, 16, 22}? D. 16 A B C D 5-Minute Check 1

A. B. C. D. A B C D 5-Minute Check 2

A B C D Solve (6 – 42 ÷ 7) + k = 4. A. 6 B. 4 C. 0 D. –1 5-Minute Check 3

Solve (3 + 42 – 9)m = 90. A. 15 B. 10 C. 9 D. 5 A B C D 5-Minute Check 4

A B C D Solve 8a – (15 – 3.2) = a + (52 – 13). A. 3.8 B. 3.6 C. 3.4 5-Minute Check 5

A. 896 B. 104 C. 42 D. 24 A B C D 5-Minute Check 6

You solved equations with one or two variables. (Lesson 1–5) Represent relations. Interpret graphs of relations. Then/Now

coordinate system relation domain range independent variable x- and y-axes origin ordered pair x- and y-coordinates Vocabulary

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. Example 1

Graph Graph each ordered pair on a coordinate plane. Representations of a Relation Graph Graph each ordered pair on a coordinate plane. Example 1

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 3 –1 –4 Domain Range Example 1

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}. Example 1

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

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

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. Example 2

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. Example 2

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 number of new members is the independent variable. The dues is the dependent variable. B. Membership dues is the independent variable. Number of new members is the dependent variable. C. x is the independent. y is the dependent. D. Both are independent. A B C D Example 2

B. The area of a square increases as the length of a side increases B. The area of a square increases as the length of a side increases. 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 are dependent. A B C D Example 2

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. Example 3

The graph below represents Macy’s speed as she swims laps in a pool The graph below represents Macy’s speed as she swims laps in a pool. Describe what is happening in the graph. 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. A B C D Example 3

End of the Lesson