# Real Life Problems

For the Proposal: You’re to describe a real-life setting in which a systems of equations approach would be useful. Identify a problem situation or exploration you will engage in which will require you to apply linear functions to real-life setting. For the final project, you will do all of the following steps: Describe another setting in which a systems of equations approach would be useful. Present data for an application of your choice. (This topic was submitted in your Module7 Proposal.) Be sure to cite any sources if you use outside references for ideas or data. Write a linear equation of the form y1 = mx + b for your first set of data. Graph this equation on the xy-plane and label it as y1. You may use Excel to graph, search online for graph paper options to use, or use the ‘draw’ tools in Word to plot your lines (Graphsketch.com is resource which you may find helpful when constructing your graph.) Also, be sure to include a title on the graph and labels on the x- and y-axes. Write a linear equation of the form y2 = mx + b for the other equation in your system. Graph this equation on the same graph. You will now have two lines on the same graph. These should intersect. Find the point of intersection for y1 and y2 algebraically (by setting the equations equal to each other and solving). Show your work and also plot this point on the graph. Analyze the data and explain what the intersection means, in terms of the problem. Is there a ‘best’ solution to your problem? If so, under what conditions? Conclude your project with a short summary of what you learned.

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