The Slope of a Line

The slope of a line is a measure of the steepness of the line. This is given by the ratio of the vertical change (along y) between two points of the line to the corresponding horizontal change (along x). Thus, we have, the slope m = (change in y)/(change in x) = (y_2 - y_1)/(x_2 - x_1) IMPORTANT POINTS:
  • The slope between any two points of a given line is constant.
  • Since a unique line is determined by two points, then a line may be uniquely determined by a point and the slope of the line.
  1. Point P can be moved freely around the Cartesian Plane. Points A and B are points fixed on the given line.
  2. The slider adjusts the slope of the given line.
  3. Move the points A and B along the line. Observe how the slope remains unchanged between them.
  4. Change the value of the slope m of the line. What observations can you say about the line for certain values of the slope?
    • What can we say about the line when m>0?
    • What can we say about the line when m=0?
    • What can we say about the line when m<0?