It’s time to begin thinking about the final project and forming the framework which will guide your work. The final project will focus on linear functions and using them in a system of linear equations.

Exploring and solving systems of equations form the basis of the Final Project.

For the Proposal: Describe a real-life setting in which a system 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.

In the final project, you will perform all of the following steps:

Restate your scenario (submitted and approved in this assignment).

Present data for an application of your choice. (submitted and approved in this assignment.) 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.

Please take a moment to review the final project guidelines in Week 14 and the sample given below. Then present your final project proposal here. Taking the time to lay out your ideas for the final project will help ensure that the project you’ve chosen is appropriate and will also help you create a well organized, well executed project in the final weeks of our course. Be sure to also take a look at the final project rubric found in Week 14.

For the final project proposal in this assignment, please include:

Statement of the problem you intend to solve. Here you would explain the problem, why its important and what you hope to learn/analyze.

Data or equation you intend to analyze. Here you should present data that you will gather or data the you have found on a particular website. Alternatively, you may wish to explore equations presented in our textbook or found on the internet. You could change one or more parameters and assess how the model changes.

Ideas to get you started:

Saving the environment: A hybrid vehicle costs more than a conventional vehicle, but can save you money each year on the cost of gasoline. Which vehicle is a better deal over the life of the vehicle? Which assumptions are used and how does changing the assumptions change your answer?

Time to celebrate: Looking for a venue to hold an event, such as a wedding, involves a lot of research. These venues often have an initial booking fee along with a plate fee for each guest. Using a linear system of equations can help you determine the most economical option.

Weight loss: If two friends are on a weight loss challenge together and they start at different weights, and each consistently loses the same amount of weight per week, can they ever end up weighing the same amount? A linear system of equations can model this scenario.

Our textbook contains many applications and ideas. You may wish to use a linear system of equations example to further expand on. Note: Solving a textbook problem does not meet the requirements for this project. However, exploring a model presented in the book and adding additional analysis, research or data could lead to a wonderful project.