This is done in order to decrease the uncertainty (error).
In an ideal scenario the points are infinitely small, the lines are infinitely thin, and you can find the coordinates of the two points with any precision you want. In that ideal life the two points can be as close as you want, the distance does not matter.
Real life unfortunately is a lot messier. Let us work out an example.
Your line has a slope of 91/97 or 0.938144329896907… and (to make it simple) it goes through origin (x=0, y=0), which will be your first point. You need to pick the second point.
- Let us pick a point which is close-ish to the first point. For example x = 5.0 mm (as measured by a mm ruler, the last digit being an estimate). The y coordinate is somewhere between 4 and 5 mm, closer to 5 than to 4, so you estimate it as 4.8 mm. That gives you the slope of 0.96 (you can only have 2 significant figures). That’s an error of about 2%. Not too bad, but not ideal.
- Now let us pick a point as far as possible from the origin. For example x = 100.0 mm (10 cm is pretty normal size for a graph). The y coordinate is somewhere between 93 and 94 mm, closer to 94 so you estimate it as 93.7 mm. That gives you the slope of 0.937 (you are allowed to keep 3 significant figures). That’s an error of about 0.1%. Much better than 2%!
- If the graph was made on graph paper you may have noticed that it goes through the point x = 97.0 mm, y = 91.0 mm. That point (fairly far from origin, right?) would give you the slope of 0.938. That’s an error of about 0.02%. Wow!
