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2.1 Line of best fit
2.2 Conversion non-linear line to linear line
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To draw a line of best fit
All the points close to each other
The line pass through as many points as possible.
Number of points that not plotted above and belowthe line is
about the same, and also almost same
distance from the line.
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The power P watts and voltage V volts produced by an
electric
generator are connected a relationship in the form P = mV + n
where
m and n are constants. The following values were obtained in
an
experiment. I
a) Plot P against V and draw the line of best fit.
b) Then, determine the linear law connecting P and V
c) Determine the value of P when V = 25 V
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(b)
(c)
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130
ques
(c)
(b)
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b) P = mV + n
y = mx + C
c) P = 130
ques
graph
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2.1.3
Determining values of variables from
equations of lines of best fit
The diagr
am shows a straight line
passing through two points. Find
the linear equation connecting the
variables S and x. Then, determine
a) the value of S when x = 0,
b) the value of x when S = -18.
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Exercise 2.1
# 5, 6, 7
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2.2 Conversion non-linear line to linear line
8
Non-linear line
Convert to
linear line
linear line
A non-linear equation can be reduced tothe linear form Y = mX +
c
so that a straight line graph is obtained
when we plot Y against X.
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Example 5 (pg 38)Reduce each of the following non-linear
relation to the linear form
Y = mX + c where m and c are constants:
9
Try to cancel xtoget constant
number without x.
Y = mX + c
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Example 5 (pg 38)
10
Reduce each of the following non-linear relation to the linear
form Y =
mX + c where m and c are constants:
Y = mX + c
Try to cancel xtoget constant
number without x.
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Example 6 (pg 38)Reduce the following non-linear relation to a
linear form by taking
logarithms to base 10.
11
xba
xaabbx
1010
101010
loglog
loglog)(log
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Exercise 2.2 #1, 2
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Determine non-linear equation from linear graph
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Y = mX + c
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Determine non-linear equation from linear graph
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Exercise 2.2
#3, 4(b)(d), 5
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Determine non-linear equation without graph
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Exercise 2.2
#6, 7
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2.2.3 Graph of linear line
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a) Plot and draw the best fit line for log10yagainst log10x.
b) From you graph, determine the values ofaand n
c) From you graph, find the approximate value ofx when y
= 63.
The following table shows the experimental values of the
variables x
and y which are related by an
a)
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a)
log10x
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Y = m X + C
b)
3.09
3.09
c)
4.57
Exercise 2.2
# 9, 12
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