Lial/Hungerford/Holcomb/Mullins: Mathematics with Applications 11e Finite Mathematics with Applications 11e Copyright ©2015 Pearson Education, Inc. All right reserved.

Graphs, Lines and Inequalities Chapter 2 Graphs, Lines and Inequalities Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved. Section 2.1 Graphs Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved. Example: Sketch the graph of Solution: Since we cannot plot infinitely many points, we construct a table of y-values for a reasonable number of x-values, plot the corresponding points, and make an “educated guess” about the rest. The table above shows a few x-values and y-values. Sketch the line that connects the points. The graph above shows the points on the coordinate plane. The points indicate that the graph should be a straight line. Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved. Section 2.2 Equations of Lines Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Find the slope of the line through the points Example: Find the slope of the line through the points Solution: Let Use the definition of slope as follows: The slope can also be found by letting In that case, which is the same answer. Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved. Section 2.3 Linear Models Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved. Example: Social Science Two linear models were constructed from data on the number of full-time faculty at four-year colleges and universities: For each model, determine the five residuals, square of each residual, and the sum of the squares of the residual. Solution: The information for the first model is summarized in the following table: Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved. Example: Social Science Two linear models were constructed from data on the number of full-time faculty at four-year colleges and universities: For each model, determine the five residuals, square of each residual, and the sum of the squares of the residual. Solution: The information for the second model is summarized in the following table: Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved. Example: Social Science Two linear models were constructed from data on the number of full-time faculty at four-year colleges and universities: For each model, determine the five residuals, square of each residual, and the sum of the squares of the residual. Solution: Compare the two models by looking at their squared residuals. According to this measure of the error, the line is a better fit for the data because the sum of the squares of its residuals is smaller than the sum of the squares of the residuals for Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved. Section 2.4 Linear Inequalities Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved. Example: Solve Solution: Add to both sides. Add to both sides. To finish solving the inequality, multiply both sides by . Since is negative, change the direction of the inequality symbol: The solution set, , is graphed below. The bracket indicates that is included in the solution. Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Polynomial and Rational Inequalities Section 2.5 Polynomial and Rational Inequalities Copyright ©2015 Pearson Education, Inc. All right reserved.

Use the graph of below to solve the inequality Example: Use the graph of below to solve the inequality Solution: Each point on the graph has coordinates of the form The number x is a solution of the inequality exactly when the second coordinate of this point is positive—that is, when the point lies above the x-axis. The solution of the inequality can be determined from the graph by noting the x-values for which the curve is above the x-axis. and when The graph is above the x-axis when So the solutions of the inequality are all numbers x in the interval or the interval Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.