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How are different types of relationships represented graphically and algebraically? Compare and contrast the similarities and differences in the graphs drawn and their algebraic representation. Different types of relationships are represented graphically and algebraically between an independent variable and a dependent variable, In this case, the independent variable is time ( in mins) and the dependent variable is temperature ( in c ). as time increases, the temperature of both water and ethanol decrease . upon graphing the data , the patterns show decreasing linear trends, which are also supported by the algebraic expressions found . The rate at which ethanol cooled down was slightly faster than the rate at which water cooled down because the algebraic expression for ethanol had a slightly steeper slope than the slope of algebraic expression for water . Graphing data allows for a better representation of patterns between the data and makes it easier to create algebraic expressions to find the line of best fit with respect to the data collected d from the experiment. water ( time vs temp) digebraic expression interpreted - y= - 2.21x + 60.20 as time increased , the temp of the water decreased by - 2.21 Ethanol ( time vs temp ) algebraic expression interpreted y=- 2.40* +60.80 as time increased, the temp of the ethanol decreased by - 2.40 18

GRAPHING RELATIONSHIPS-Exp. B-3 Name Lab Section Lab Partner Problem Statement: How are different types of relationships represented graphically and algebraically? I. Data Collection: F vs. "C Arrange a ring stand with a ring, wire gauze, and a 250 ml beaker half filled with water, Measure a temperature of the water with a Celsius and a Fahrenheit thermometer (to+0.2). Be careful to measure the temperatures at the same time and don't let the thermometers touch the glass walls of the beaker when measuring the temperature. Measure the temperature five more times after having varied the temperature by heating or cooling the water. Record the data obtained in the table. WATER ETHANOL WATER ETHANOL 140, 360 141440 60.20 60.80 131. 720 134:780 55. 40 57, 10 123. 440 124 . 340 m 50. 80 51, 30 114. 420 11 560 45.90 44. 20 + 2 107, Dead 104 900 41.70 40 . 50 100 .580 98. 240 38. 10 36. 80 + 2 II. Data Analysis What patterns are shown in these data? It might be helpful to graph the data. Try to come up with an algebraic equation that expresses the pattern you found. ETHANOL WATER 70.00 (0: 60.20 ) (0, 60.80 ) bo.00! ( 2, 55. 40) 6 60.00 ( 2 , 57: 10 ) temp 5.0,00 (4, 50.80 ) ( 4, 51. 30 ) $50.00 ( 6. 45.90 ) ( 6 , 44. 20 ) 40.00 (8, 41. 70 ) 40.00 (8, 40,60 ) (10, 38, 10) (10, 36.80) 30,co 30,00+ 2 10 m= 40.20-38.10 Time (mins ) m = 60.80- 36.80 Time ( mins ) = - 2.40 10 - 10 = - 2.21 15 10 - 10 y=- 2.21x+ 60.20 6= (60. 8)- (-2.40) (0 ) y = -2.40* +60. 80 b= (60. 20) - ( - 2. 21) (0 ) 6 = 60.80 6 = 60.20 WATER ETHANOL

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