1. Graphs & Line (Curve) of Best Fit

2. Line (Curve) of Best Fit

3. Line (Curve) of Best Fit
When data is displayed with a scatter plot, it is often useful to attempt to represent that data with the equation of a straight line (or curve) for purposes of predicting values that may not be displayed on the plot.
A line (or curve) of best fit is a straight (or curved) line that best represents the data on a scatter plot. This line (or curve) may pass through some of the points, none of the points, or all of the points.

4. Example: Applied Force vs. Elongation
1. Plot the data points for force vs. elongation.
The following data were obtained by varying the force applied to a spring and measuring the corresponding elongation of the spring.
0.20
0.40
Elongation (m)

5. Example: Applied Force vs. Elongation
This slope shows the speed of the process, i.e. for every 30 N the spring elongates by 1 m.
2. Draw the best-fit line.
3. Using the best-fit line, determine the spring constant of the spring.
rise=19N-10N=9N RT
run=0.65m-0.35m=0.30m
run=.65m-0.35m=0.30m
rise=19N-10N=9N
0.20
0.40
Elongation (m)