I'm making a graph of force vs stretch for springs. I have 7 data trials with the k (F = kx) ranging from 28 to 31, average is 29.6.

Now I need to find the slope and write an equation for the graph. If I use the first two points to get the slope, I get a slope of 29.4. If I use the first point and the last point, I get a slope of 28. I understand the larger interval would give the best value, but using the first two points to compute it gives a slope closer to my "k" value. I know the slope is my spring constand or k value so they should be close.

Question is: which interval should I use: first and second points or first and last points to compute the slope.

You should use all three and minimize the square error when fitting a straight line through the origin.

It's called a linear regression best fit.

This will also give you an error estimate.

So my slope doesn't have to be so exact to the k value?

When I use the equation to predict the stretch, I get a value of .085 using the first two points and a value of .089 when using the first and last points. The given data table lists the actual stretch at 0.085.

So in showing my work, which 2 points should I use?

You should use all seven of your data points, and a linear regression curve-fitting technique. There are tools online at places like

http://people.hofstra.edu/Stefan_Waner/RealWorld/newgraph/regressionframes.html

To determine which interval you should use to compute the slope, you need to consider the purpose of finding the slope and what it represents in your graph.

The slope of the graph represents the relationship between the force (F) and the stretch (x) of the springs, which is given by the equation F = kx, where k is the spring constant. The slope essentially quantifies this relationship, with a steeper slope indicating a larger spring constant.

In your case, you have 7 data trials with the spring constant ranging from 28 to 31, with an average of 29.6. By comparing the two potential interval choices, we can determine the most suitable one.

1. Using the first two points: By computing the slope between the first two points, you get a slope of 29.4. This value is closer to the average spring constant, which suggests a better fit with the overall trend of your data. However, it's important to note that using only two data points may not accurately represent the entire range of your data.

2. Using the first and last points: By computing the slope between the first and last points, you get a slope of 28. This value is farther from the average spring constant, indicating a lower spring constant than expected. However, using the first and last points captures the full range of your data, providing a more comprehensive representation.

Considering this information, it seems more appropriate to use the first and last points to compute the slope. Although the slope obtained might not match your average spring constant as closely as the other option, it is based on a larger interval, providing a better representation of the overall trend of your data.

It's worth mentioning that using only two data points to estimate the slope might not be the most accurate approach. If possible, consider using regression analysis or fitting a line through all the data points to obtain a more precise slope value.