Solve for the intersection of the two straight lines.

Try first to solve by deductive reasoning and visualization. Using the graph on the webpage as a guide, visualize how the listed functions will change the graph. Determine an approximate location of your visualized intersection. Then choose from the list of intersecting points that best match your visualization. Deductive reasoning can also be used to rule out solutions that are obviously not for a particular pair of straight lines. It is quite possible to solve this set of problems without doing any calculations!

If visualization and deductive reasoning do not work for you yet, find the intersection by mathematical techniques you already know. Set y1 = y2, then solve for x. As you are doing these calculations, you will observe how the small changes in the straight line formulae affect the final results. These observations are building your skills for seeing numerical patterns. As you develop this skill, your skills for deductive reasoning and visualization will improve. Return to this website a month later (when you forget all the answers) and try to solve without doing any calculations.

Dave’s Math Challenges can be solved very easily with a graphing calculator. But you would not be developing any new skills if you choose this method.