How to draw a line of worst fit?

Here is the question that I am currently stuck on. I don't know how to do part (b) of the question above, especially part (i) of (b) which asks for an extreme fit line for the points. I've read that you need error bars drawn with your points to do this. Will I need them? Otherwise how would I go about drawing the line of worst fit? ....

....Also, I would appreciate it if somebody could go over part (ii) of (b) which concerns uncertainty. It's something I've only begun revising recently so it would be helpful if you could show me (and any others who may struggle with uncertainty in general) how to do it for this question.

I am not sure which examination board are you taking. Drawing the line of worst fit should involve the usage of the error bar. However, if the error bars are not present, I believe you can still draw the extreme fit line as shown below.



There is generally no strict rule in attempting to draw line of worst fit. (IMO is like an art of drawing the line of worst fit.) The way that I draw is to find the midpoint for the best fit line (when there are no error bars). When I tilt the ruler to see if the ruler can pass through other points that the best fit line does not pass through, the ruler would pivot about the midpoint.

Different people have different of drawing line of worst fit.
https://www.youtube.com/watch?v=9_qxohScVbk
https://www.antonine-education.co.uk/Pages/Induction/Induction_6/Induction_Page_6.htm

The examiners generally would not be very strict about the way you draw when no error bar is present. But when error bars are present, the marking would be more strict.





As for (b)(ii), you need to extend both the best fit line and extreme fit line to cut the y-axis to read the y-intercepts for the best fit line and extreme fit line respectively.
Say the y-intercepts for the best fit line and extreme fit line are y_b and y_e respectively.

The uncertainty in the original length = $|y_b – y_e|$

Thank you so much! I really appreciate your thorough explanation and diagram. Thanks for taking the time to provide this. I will have another go at this today!