(Algebra > Relations & Functions > Functions)
In our previous document Introduction to Slope, students learned that the ratio of the vertical distance to the horizontal distance between two points describes the slope of a line. In this document, Calculating Slope, we allow students to explore common errors when computing slope.
The important concept here is for students to recognize that subtracting the y-coordinates of two points finds the vertical distance and subtracting the x-coordinates finds the horizontal distance. Students get a chance to explore the order in which they subtract points—leading them to understand that it does not matter with which point they begin, as long as they subtract coordinates in the same order.
As students investigate the slope between different points on the same line, they also come to the realization that the slope is always the same between any two points on the line.