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# Class Note for MATH 2303 at UH

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This 9 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 17 views.

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Date Created: 02/06/15

Math 2303 Applications 7 Linear Equations Graphing Plotting Points Method Graphing Intercept Method We use mathematics to model real world situations In this lesson we ll solve some applications using linear equations Example 1 Suppose your textbooks cost 33995 including tax one semester You only have 350 to spend on books and supplies and the only supplies you need are spiral notebooks The bookstore is selling spiral notebooks for 099 tax included How many notebooks can you buy if you stay within your 350 budget Example 2 Thirtytwo hours of overtime work will be split among three workers One worker will be assigned twice as many hours as each of the other two How many overtime hours will be assigned to each of the three workers Example 3 Bill has 80 feet of fencing to use to fence in a dog run for his pet dog He wants the dog run to be 5 feet longer than it is wide What should be the dimensions of the dog run Example 4 There has been a signi cant increase in the number of taxpayers who le their tax returns electronically In 2006 387 million taxpayers led electronically In 2007 that number was up 141 How many taxpayers led electronically in 2007 Example 5 The total oor space in three barns is 45000 ftz The two smaller barns have the same area but the larger one is three times the area of each of the smaller ones a Determine the oor space for each barn b Can merchandise that takes of 8500 ft2 of oor space t into either of the smaller ba1ns Example 6 A health club is offering two membership plans Plan A costs 56 per month for unlimited use Plan B costs 20 per month plus 3 for each visit How many visits would you have to make each month to make Plan A cost exactly the same as Plan B If you knew you would use the 25 times a month which plan should you pick If you thought you d only go twice a week would that change your answer Graphing Linear Equations So far we have only looked at equations with one variable Many real world situations require the use of two or more variables For example pro t depends on both costs and revenues 7 that situation contains three variables We re going to work with some equations in two variables We ll use x and y as the variables for convenience We want to be able to graph these equations in the coordinate plane y You should be able to plot points in the coordinate plane Example 7 Plot each ordered pair in the coordinate plane A 23 B 4 1 C 40 D 04 E 2 0 F 0 2 G 1 3 H 4 2 Y 4 3 2 1 I I I I I I 41 73 72 71 1 71 72 73 4 Example 8 Points A B and C are three vertices of a parallelogram Plot them in the coordinate plane and then determine the coordinates of the fourth vertex A1 2 B2 4 C7 4 y 4 All equations ofthe form ax by c a 72 0 b 72 0 can be graphed in the coordinate planes Their graphs will be straight lines You can graph an equation in two variables by plotting points You ll nd several order pairs of points that lie on the graph of the equation and then connect the points with a line Example 9 Fill in the table of values and then graph the linear equation 3x y 5 X L l 0 2 Y 4 3 2 1 x I I I I I I I I l I I I I I I I I I I 4t 73 72 71 1 2 3 4 1 2 3 4 Plotting points works but it is very tedious We really only need two points to determine a line Here is another method that is usually quicker and more ef cient than just plotting random points We can graph an equation using the X and y intercepts To do this ll in this table and then graph the points and connect them with a line Example 10 Use the method of intercepts to graph 2x 4y 8 4 0 4 1 Example 11 Use the method of intercepts to graph 3x 2 y 6 3 1 73

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