For example, the Slope-intercept Form activity shown below simplifies the process of drawing graphs of straight lines. This allows students to focus on the relationships between the coefficients of the equation and its graph.
Students can plot graphs by hand, using a table of values and then plotting points.
But if the object of the lesson is to understand the effect of m and b, then this would be a cumbersome process. In particular I would welcome ideas for discovery-based learning. Brian Sharp from the United States suggested using the Vector Addition activity from ExploreScience . The best way that I have found to motivate students to learn about vectors is to pose real-life questions to them. After several questions of this type students come to realize that understanding vectors is absolutely essential to their activities in everyday life.