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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

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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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