MATH 1711: WEEK 8

Topics for this week are:

• Lines and the Cartesian Plane
• Inequalities
• The Method of Least Squares

Objectives for this week:

• Find the equation for a line using any of the three basic forms
• Graph lines in the plane
• Find the intersection of any two lines
• Graph and shade the feasible set for a system of inequalities
• Find the least-squares line to best fit a group of data points

Text coverage:     Sections 1.1 - 1.5 of Goldstein, Schneider and Siegel, with emphasis on 4.3 - 4.5

Online resources:

• Week 8 Formula Sheet
• Week 8 Practice Problems
• Online notes
  • Notes on the Cartesian plane and lines. Here is a brief review of the Cartesian plane and various forms of linear functions. We learn the equations of circles and lines, and find the intersection of two lines.
  • Using a spreadsheet to plot straight lines.In this course, we will work with various applications of linear equations. In this worksheet, you will learn how to plot straight lines using Microsoft Excel.
  • Using a spreadsheet to find the intersection of two lines.Many of the procedures we will learn involved finding solutions to systems of equations. In two dimensions, our solution is simply the intersection of two lines. Use this worksheet to learn how to find the intersection of two lines, given in slope-intercept form, on your spreadsheet.
  • Notes and applications on Supply and Demand equations. We examine some linear supply and demand curves, and discuss the meaning of market price and equilibrium.
• Maple Worksheets
  • A Maple worksheet on graphing the feasible set of a system of inequalities.  We learn how to use Maple to help graph the feasible set of a system of inequalities and find the corner points of the feasible set.
  • A Maple worksheet on the least-squares problem. We explore the solution to the least-squares problem using Maple's matrix operations. Given n data points, we wish to find the line, y=mx+b, that "best fits" the data. Transforming our data points into matrices yields a matrix equation Y=AX. Our goal is to solve for the matrix X. Since our matrix A is not a square matrix, we multiply both sides by the transpose of A and then use previously learned methods to solve the system. As an example, we try to find a linear relationship between high school and college GPA's.

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Last Modified: . School of Mathematics, Georgia Institute of Technology.