Temperature Experiments
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1 Name Hour Temperature Experiments A group of scientists are conducting experiments where they must raise and lower the temperature steadily. The starting temperatures of their experiments may also vary. Section 1: Starting Temperature and Rate of Change on Tables, Graphs and Equations For each scientist in questions 1-4, write an equation to represent the scenario, and then create a table of values and a graph. The domain should include at least 4 values, and 1 of these values must be 0. Use x to represent number of minutes, and y to represent temperature. Scientist A has been completed for you. Scientist A has a starting temperature of 10 0, and raises the temperature steadily 5 0 every minute. y = 5x Scientist B has a starting temperature of 2. Scientist C has a starting temperature of -5 0 and raises the temperature 10 0 every minute and lowers the temperature 5 0 per minute. Table: Table: Equation: Equation:
2 3. Scientist D has a starting temperature of 4. Scientist E has a starting temperature of 0 0 and raises the temperature 10 0 per of and lowers the temperature 5 0 per minute. minute. Table: Table: Equation: Equation: 5. How does the starting temperature show up in the table? In the graph? In the equation? 6. How does the rate at which the temperature changes each minute show up in the table? In the graph? In the equation? 7. How can you tell if the temperature is rising or falling in the table? In the graph? In the equation?
3 Section 2: Comparing and Analyzing Data The data below is from several different scientists, using x for time in minutes and y for temperature in degrees Fahrenheit. Use the data to answer questions Scientist A Scientist B Scientist C Scientist D Scientist E Scientist F Scientist G Scientist H y = 2x + 20 f x = 15x + 10 y = 10x 8. Which scientists have decreasing temperatures in their data? How can you tell? 9. Which scientists have increasing temperatures in their data? How can you tell? 10. Which scientist has the temperature that is increasing at the fastest rate? Slowest rate? 11. Which scientist has the temperature that is decreasing at the slowest rate? Fastest rate? 12. Which scientists have temperatures changing at the same rate? How would this appear on a graph?
4 13. What scientist starts with the highest temperature? Lowest? How can you tell? 14. On a graph, the y-intercept represents the point where the line crosses the y-axis. On a table, it is the corresponding y-value when x is equal to zero. In this data, what would the y-intercept represent? 15. On a graph, the x-intercept represents the point where the line crosses the x-axis. On a table, it is the corresponding x-value when y is equal to zero. In this data, what would the x-intercept represent? 16. All of this data is linear. What does that mean? How does it show up on the table and graph? 17. Select all of the equations below that would be linear. How did you know? a.) 5x + 10 = y b.) y = 3x + 2 c.) 3xy + 10 = 100 d.) 2x 2 = Scientist H is represented by the equation y = 10x. What is his starting temperature? Is there a way that you could incorporate his starting temperature into the equation? Section 3: Finding Rate of Change/Slope Figure the rate of change in degrees per minute for each scientist for questions You will need to consider the amount of temperature change/number of minutes. X represents time in minutes and y represents temperature in Fahrenheit. 19. Scientist A collected data twice and represented his data with the following ordered pairs: (4, 20) and (10, 32). 20. Scientist B collected data twice and represented her data with the following ordered pairs: (2, -4) and (10, 0). 21. Scientist C collected data twice and represented his data with the following ordered pairs: (3, 5) and (6, -10 ).
5 22. Scientist D represented her data 23. Scientist E represented her data below. below. 24. Scientist F represented his data 25. Scientist G represented her data below. below. 26. Scientist H represented his data with the equation y = 4x Scientist I represented her data with the function f x = 2x Look at the graphs below. Interpret what they would mean in terms of our context. Could either graph make sense?
6 Slope Formula: Positive means Negative means Positive means Negative means m is slope (rate of change) y = mx + b b is the y-intercept (starting amount) How does it show up on a table? graph? equation? How does it show up on a table? graph? equation? Undefined slope
7 Definition Characteristics Examples domain Non-examples Definition Characteristics Examples range Non-examples
8 Definition Characteristics Examples coefficient Non-examples Definition Characteristics Examples y-intercept Non-examples
9 Definition Characteristics Examples x-intercept Non-examples Definition Characteristics Examples slope Non-examples
10 Name Rate of Change/Slope Practice Identify the rate of change or slope for each situation Hour dollars/t-shirt meters/second What is the slope of the line y = 4x + 1? 5. What is the slope of the line y = -2x? meters/seconds cost/pizza topping donuts/pack 8. What is the slope of the line passing through (2, 5) and (6, 25)? 9. What is the slope of the line passing through (4, 16) and (10, 4)?
11 Name Equation Writing Practice Hour Kelly is buying a charm bracelet. The bracelet costs $12, and each charm costs $5. Complete the table and graph below. Then write an equation to represent the situation, and identify the slope and y-intercept. Charms Finding the Total Cost Total Cost Equation: Slope: Y-intercept: Tim is buying a pizza. It costs $8 for a plain pizza with no toppings. Every topping adds $0.50 to the cost. Complete the table and graph below. Then write an equation to represent the situation, and identify the slope and y-intercept. Toppings Finding the Total Cost Total Cost Equation: Slope: Y-intercept: Tom has $500 and spends $25 each week. Equation: Slope: Y-intercept: T-shirts sell for $6 each. There is a one-time set-up fee (flat fee) of $20 for any number of shirts. Equation: Slope: Y-intercept:
12 Name Slope and Y-Intercept Practice Hour x y x y x y x y Slope: Slope: Slope: Slope: Y-intercept: Y-intercept: Y-intercept: Y-intercept: Equation: Equation: Equation: Equation: Slope: Slope: Slope: Y-intercept: Y-intercept: Y-intercept: Equation: Equation: Equation:
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