# Uncertainty of a straight line

## Homework Statement

My teacher assigned a lab report on an experiment where 2 graphs need to be drawn. One graph has some uncertainty which is calculated alright ((slope max - slope min) * 0.5) and the other graph still need to be drawn.. The values of the second graph make a perfect straight line which would make the uncertainty to be 0. how would you calculate the uncertainty?

## The Attempt at a Solution

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Hi there,

Are you absolutely sure that the graph make a perfect straight line. That would mean that all you experimental measures are precisely on the line. If so, from your experimental measures, you would have not uncertainty.

Just because the data points fit on a straight line does not mean that there was no uncertainty in the measurements.

You should have error boxes around each point, based on the uncertainties in the measurements of your variables.

Hi there,

These uncertainties are considered in the measurements of the points.

There is no added uncertainty to the plotting of the graph.

Cheers

Either I am not understanding this properly, or fatra knows more about the specific task you have been given.

Maybe you could shed some more light on the experiment that you are required to be writing up.

But consider an experiment on Hookes' Law:
You hang weights from a spring and measure the distance it stretches.

To find the spring constant of the spring, you can plot distance vs. weight and find the gradient. The uncertainty in your value for the spring constant can be found by the uncertainty in the gradient of the graph. This can be done as you have described above.

You will have uncertainty in the measurements of weight and in the measurements of distance. These values should allow you to set up error boxes around each point. It is using these boxes that can give you max and min gradient.

Your measured values might end up lying on a straight line - but this does not mean that there is no uncertainty in your measurements!