Given a straight line plotted on a graph we can
estimate the values of the gradient and either using a point on the
line or by estimating the y – intercept, we can find the equation
of the line in the form
The
most convenient form in which to analyse the relationship between two
variables x and y is the linear form, and we must see if, given a
suspected relationship between two variables, we can construct a
linear graph from the suspected relationship.
The
most convenient form in which to analyse the relationship between two
variables x and y is the linear form, and we must see if, given a
suspected relationship between two variables, we can construct a
linear graph from the suspected relationship.
Suppose we suspect an exponential relationship between
two variables. We also have the following data.
|
Time, t in s
|
10
|
20
|
30
|
40
|
50
|
|
Mass m in g
|
40.3
|
27
|
18
|
12.2
|
8.1
|
Our relationship will take the form
To
transform this into a straight line we take logs of both sides
obtaining,
We
recalculate the table.
To
transform this into a straight line we take logs of both sides
obtaining,We
recalculate the table.|
Time, t in s
|
10
|
20
|
30
|
40
|
50
|
|
log (m)
|
3.696
|
3.296
|
2.890
|
2.501
|
2.092
|
with
we
see
so
and
so
then
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