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OpenStudy (michele_laino):
we have y = temperature, and x = time
we have to conjecture thi relationship:
y=ax+b
OpenStudy (michele_laino):
now I use the numerical data of the problem, so I can write:
\[\left\{ \begin{gathered}
66 = 5a + b \\
87 = 12 + b \\
\end{gathered} \right.\]
OpenStudy (michele_laino):
we have to solve that system
OpenStudy (howard-wolowitz):
ok
OpenStudy (howard-wolowitz):
ok well thats a fraction
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OpenStudy (michele_laino):
try to solve the first equation for b, please
OpenStudy (howard-wolowitz):
a= -b/5 + 66/5
OpenStudy (michele_laino):
ok! Now substitute that value for a into the second equation
OpenStudy (howard-wolowitz):
ok
OpenStudy (michele_laino):
\[\left\{ \begin{gathered}
66 = 5a + b \\
87 = 12a + b \\
\end{gathered} \right.\]
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OpenStudy (howard-wolowitz):
b=75
OpenStudy (howard-wolowitz):
a = -b/5 + 66/5
OpenStudy (michele_laino):
please wait I'm checking your value of b
OpenStudy (howard-wolowitz):
ok
OpenStudy (michele_laino):
I got b= 51
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OpenStudy (howard-wolowitz):
well i wasn't right then
OpenStudy (michele_laino):
no problem.
Now we substitute b=51 into the first equation, and we get: a=3
OpenStudy (michele_laino):
please wait a moment
OpenStudy (howard-wolowitz):
ok
OpenStudy (howard-wolowitz):
@epoweritheta
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OpenStudy (howard-wolowitz):
@Sparklestaraa
OpenStudy (howard-wolowitz):
@welshfella
OpenStudy (howard-wolowitz):
@phi
OpenStudy (howard-wolowitz):
I think its A
OpenStudy (phi):
a snapshot of the screen as a png file is way faster to look at than the .doc file.
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OpenStudy (phi):
your choices are equations of a line
First step:
look at the data, and make (x,y) pairs
for example (5,66) (at 5 it's 66)
and (12, 87) (at noon, 12 o'clock, it's 87)
now you have two points
now do the usual thing:
find slope = change in y divided by change in x
then find the y-intercept.
OpenStudy (phi):
in other words, this problem is finding the equation of a line, starting with 2 points.
Do you know how to do that, or do you need help?
OpenStudy (howard-wolowitz):
hmm OK one sec........ i got 51 with Michele help and thats the y intercept, correct?
OpenStudy (phi):
I would first find the slope
(87-66)/ (12-5)
OpenStudy (howard-wolowitz):
ok then thats 3
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OpenStudy (howard-wolowitz):
so its A cause 3 is 3x
OpenStudy (phi):
so you start with
y= mx +b
m is 3
y = 3x + b
now use (5,66) to find b:
66 = 3*5 + b
66= 15+ b
OpenStudy (howard-wolowitz):
i see why we find slope first
OpenStudy (phi):
The idea was notice we could list two points, then we can use our knowledge of how to find the equation of a line through 2 points.