Thread: help with non linear laws and plotting them.

Hi, I have been learning about graphical techniques, rearranging equations so they can be plotted on linear and log graph paper and things like that. I’ve been told if the law is in the form y=(a/x) +b then if y is plotted against 1/x a straight line graph is produced where a is the gradient and be is the intercept.

aswell as if y=ax²+b and x² is plotted against y a straight line is formed where a is the gradient and b is the intercept.

I’ve been given 2 examples but can’t seem to get the correct answer. I’ve been plotting these on normal graph paper and I’m not sure if that is what I’m doing wrong?

q1)

an experiment connected with the flow of a water over a area gave the following results

f	0.503	0.454	0.438	0.430	0.425	0.421
t	0.1	0.2	0.3	0.4	0.5	0.6
1/t	10	5	3.33	2.5	2	1.6

The relationship between f and t is thought to be f=a/t+b. test if so and find the values of a and b


Q2) the current for wires of various diameter is shown below

d(mm)	5	10	15	20	25
i amps	6.25	10	16.25	25	36.25
d2	25	100	225	400	625

it is suggested this data follows I=ad²+b. by plotting a graph show that the law holds and find the constants a nd b


any help with solving these would be great, I’m not sure if i have to use normal graph paper or log log paper?

on another note if I use the data in the table is there a way of working out the values with out plotting the graph

any help would be truly appreciated.

Thanks

You should be using normal graph paper.
'Real data' is subject to experimental error so you mustn't expect all of the points to fit your result exactly. Having plotted the points you draw in what you think to be the best straight line. Different people may have different opinions as to what is the best straight line and so arrive at slightly different results.

Originally Posted by djstar

an experiment connected with the flow of a water over a area gave the following results

f	0.503	0.454	0.438	0.430	0.425	0.421
t	0.1	0.2	0.3	0.4	0.5	0.6
1/t	10	5	3.33	2.5	2	1.6

The relationship between f and t is thought to be f=a/t+b. test if so and find the values of a and b

Perform a linear regression on the data 1/t vs f on a graphing calculator. I also believe Excel will do this also.

Thanks you both for the replies, i got the same value as skeeter did for a, because i can use the actual data in the table for this how ever my value for b was slighty of which was due to my gaph.

once again many thanks for the help.