In mathematical aspect, graphs are more than just beautiful images. From a graph, we can easily find two points. From the points, we can determine the distance, and the midpoint and the slope of the segment connecting them. As graphs become more and more complicated, you will be asked to apply and use all three of these pieces of information.
Finding the distance
Distance is a numerical description of how far apart objects are. To find the distance between two points, given the coordinates of these two points are (x1, y1) and (x2, y2), the distance D between the points is given by:
D = sqrt [(x1-x2)^2+(y1-y2)^2]
Finding the midpoint
In Geometry, the midpoint is the middle point of a line segment, which is equidistant from both endpoints. To find the midpoint of those same two points (x1, y1) and (x2, y2), all you need to do is to average the x and y values and express them as an ordered pair:
M=((x1+x2)/2, (y1+y2)/2)
Discovering the slope
The slope of a line describes its steepness, incline or grade. Slope is not only a very key concept for linear equations, but it is also important for differential calculus. The slope of the line between two points (x1, y1) and (x2, y2) is given by:
Slope = (y2-y1)/(x2-x1)
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