You have four points (-7,7), (-4,14), (-1,35), and (2,56) on a line. We are asked to find the slope of that line.
In mathematics, the slope of a line is a number that describes both the direction and the steepness of the line. Slope is often denoted by the letter 'm'.
We can make use of these two formulas:
1. The slope between two points (x1, y1) and (x2, y2) is given by (y2 - y1) / (x2 - x1).
2. The slope of a line given multiple points can be calculated by taking the average of the slopes between all possible pairs of points.
However, in this scenario, it's too complicated to calculate it this way, and we don't have a simple way to calculate the slope with more than two points directly.
So in this case we use a technique called "least squares fitting" - in essence what we are doing is constructing the best line that fits through these four points in such a way that the sum of the squares of the distances of each of the four points to the line is as small as possible.
The slope of this "best fit" line is 5.6 (rounded to one decimal place). This means that, on average, a one unit increase in the x-values corresponds to an increase of 5.6 units on the y-values over these four points. This provides the best linear approximation to the given data set.