10. mrs. cugini collected data on the hand span length and height of each of her
algebra i students. the graph below represents the scatterplot of the data for one class
part a: what is the slope of the graph?
part b: what does the slope represent?

This problem can be represented as a regression, which is a statistical modelling to estimate the relation between two variables, in this case, between span length and height of each student.

Typically, a regression analysis is formed with a group of data, like the graph shows, which are normally dispersed. So, the main objective here is to find a line that represents an average of all data, this line is gonna represent the linear function which will show the relation between variables. At the end, we could be able to calculate the slope.

However, we can directly calculate the slope using the formula attached. The problem here is that we don't have the specific number of each data, the graph just offers an approximation of it. So, we have to estimate a line which should contain the most number of points. This line is often found in the center of all data, because it represents an average (image attached).

Now, we can take two point that are on the line, and calculate the slope with this formula:

Where is the first point, and is the second point.

So, the most clear points are (6;45) and (8;60), because the others are too far of the line and are less exact. Then using this points on the formula:

Therefore the slope is 15/2.

The fact the slop resulted positive means that the two variables involved have a positive correlation, which means that they are directly proportional. In other words, when a variable increases, the other one too.

In this case, according with these results, we can say that the bigger a hand span length, the taller the student is.