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Question 115342: Along the way to the new location- you find that all the temperatures provided are in °F. You will now continue your observations- that you had done previously. To do so, you will need to solve a linear equation. The linear equation that relates °C to °F is as follows:
°F = 1.8 °C + 32.0
The following data was calculated in this way:
Temperature °F Miles east from starting point
85.2 0
84.5 15
83.6 25
Provide a plot of temperature versus distance east
Use the graph to determine the expected temperature at 75 miles east
I am completely lost on this problem, I know how to make a graph but I don't understand what they are asking for... could someone give me a little insight in solving this problem.
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Here's my interpretation of what you are being asked to do:
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Because you are to "continue your observations that you had done previously" and are told
that you will need to solve the linear equation that relates degrees Celsius to degrees F,
it sounds as if previously you gathered Celsius temperatures. Furthermore it sounds as
if you need to convert those temperatures to degrees F by plugging them into the given equation.
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Here's a sample calculation to demonstrate the use of the equation. Suppose you previously
found a temperature of 22 degrees C. You would convert that to degrees F by starting with:
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F = 1.8C + 32
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Substitute 22 for C and the equation becomes:
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F = (1.8)(22) + 32
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Multiply 1.8 times 22 you get 39.6 making the equation become:
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F = 39.6 + 32
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Add the two terms on the right side and you have 71.6. This tells you that 22 degrees C
is equal to 71.6 degrees F.
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You may have to do that to your previous temperatures if they are in degrees C because
you will be making a graph in degrees F.
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The data you are given are:
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85.2 degrees F at 0 miles east from the starting point
84.5 degrees F at 15 miles east from the starting point
83.6 degrees F at 25 miles east from the starting point
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You are to graph these three points and the words "temperature versus distance east" tells
you to make a graph showing distance on the x-axis and temperature on the y-axis.
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Label the x-axis in miles starting at 0 (the origin) and going out to somewhat more than
75 miles. This marking on the positive side of the x-axis represents miles east of the
starting point.
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On the y-axis you need to concentrate on a temperature range of around 90 degrees F down
maybe 75 degrees F. Therefore you may want to indicate a "break" in the y-axis between
the origin (0 degrees F) and 75 degrees F so that you can expand the scale of temperatures enough
to permit your graph to show temperatures down to tenths of a degree. (Hope this makes sense
to you because if you plot all the temperatures from 0 to 90 degrees F up the y-axis you
will have a difficult time showing the difference between 85.2 degrees and 84.5 degrees and
you will lose valuable detail.)
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Go to zero on the x-axis. Then go up to 85.2 degrees F and mark that point.
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Next go to 15 on the x-axis and go up to 84.5 degrees F and mark that point.
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Finally go to 25 on the x-axis and then up to 83.6 degrees and mark that point.
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(I'm not sure, but you may need to plot data that were taken or given earlier
from other
measurements or earlier data that you were given. This would be the data in degrees
Celsius that you used the conversion equation to change to degrees F.)
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Notice that the data you have plotted shows that the further east you go, the more the
temperature drops. Take a straight edge and draw a "best fit" line that runs through the
three points that you have plotted. (If you have plotted additional data points from previous
readings, you may want to consider them also in trying to determine the "best fit" line.)
By a "best fit" line I mean that if the data points are not in a straight line, you draw
a line that sort of runs down the middle of the points, establishing a trend and having
about an equal number of points above the line as below the line ... ignoring any data
points that are obviously far away from the general trend of the data. This "best fit"
line is the plot you were asked to find.
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Make sure your "best fit" line runs to the right enough so that it is extends out to about
80 miles on the x-axis. This is because you are asked to determine what temperature
you might expect to find at 75 miles to the east of the starting point. To do that you
would go to 75 miles on the x-axis, then go up to the line and at that intersection
find the corresponding temperature on the y-axis. I would expect that you would get an
answer somewhere around 80.4 degrees or so ... depending on how you place the "best fit"
line.
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Hope this gives you enough insight into the problem that you can work your way through it.
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