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This activity reinforces the relationship between the solution to a system of equations and the intersection of their corresponding graph. Generally, students begin to solve systems by using graphing and then algebra. Once a student learns to solve the system by algebra, they often forget the connection to the graph. Hence in this lab, they will use algebra first and then graph their answers.The student is asked to determine where an animal trail intersects with an access road. Given linear equations which represent the placement of the access roads, assign each person/group one or more equations representing an 'animal trail'. They will then determine where their trail intersects each of the two roads. This represents the spot where they will lay their have-a-heart trap. (A have-a-heart trap is one which is baited with food and catches the animal alive without hurting it.) After solving the systems, a graph is drawn to determine if the placement of the traps is accurate.
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Rather than giving the students all 8 equations for the animal trails, you may wish to run off separate forms which have only one or two animal trail equations.
Using a large sheet of graph paper, each group can put their traps on the graph. A different color can be used for each trap so that all the traps on road 1 are in one color and road 2 another color. For each color, the points should lie on the line for that road. The equations for the roads can then be drawn to determine which groups accurately placed their traps. Seeing all the traps line up gave my students an 'ah ha' moment.
Another option would be to give the students a graph with the roads already drawn. The first step would then be to determine the equations representing the roads. This is a good review of how to find the equation of a line from the graph.