{"id":1783,"date":"2016-06-27T02:46:11","date_gmt":"2016-06-27T02:46:11","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/?post_type=chapter&#038;p=1783"},"modified":"2018-12-26T03:32:49","modified_gmt":"2018-12-26T03:32:49","slug":"putting-it-together-graph-linear-equations-and-inequalities","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/chapter\/putting-it-together-graph-linear-equations-and-inequalities\/","title":{"raw":"Putting it Together: Graph Linear Equations and Inequalities","rendered":"Putting it Together: Graph Linear Equations and Inequalities"},"content":{"raw":"<img class=\"alignright wp-image-1475\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/03\/08220702\/2947716919_497a13c7ed_b.jpg\" alt=\"Watercolor painting\/sketch of a &quot;sad&quot; TV. On the screen is a simple frowny face.\" width=\"225\" height=\"225\" \/>\r\n\r\nJoan's uncle Devon is\u00a0a semiprofessional blogger who writes about media (he would really like to be a paid\u00a0film critic, but no one has offered yet). Recently, Devon posted a short blog piece complaining\u00a0about the number of ads on TV these days compared to\u00a0when he was younger. He was not very scientific about it, and a couple\u00a0of his\u00a0readers disputed a\u00a0claim he made and\u00a0tried to start an argument.\r\n\r\nDevon\u00a0asks\u00a0Joan, who is taking an algebra class at night, to\u00a0help him gather and cite some data to support his claim\u00a0that there are\u00a0\"way more\" TV ads now than when he was a kid. Together, they\u00a0get\u00a0online and do a little research and find a website that reports some interesting data on the number of minutes of TV commercials per hour since 2009. The data is shown below.\r\n<table>\r\n<thead>\r\n<tr style=\"height: 15px\">\r\n<th style=\"height: 15px;text-align: center\">Years Since 2009<\/th>\r\n<th style=\"height: 15px;text-align: center\">Minutes<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr style=\"height: 15.5938px\">\r\n<td style=\"height: 15.5938px;text-align: center\">[latex]0[\/latex]<\/td>\r\n<td style=\"height: 15.5938px;text-align: center\">[latex]8.5[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"height: 15px;text-align: center\">[latex]1[\/latex]<\/td>\r\n<td style=\"height: 15px;text-align: center\">[latex]9.25[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"height: 15px;text-align: center\">[latex]2[\/latex]<\/td>\r\n<td style=\"height: 15px;text-align: center\">[latex]10[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"height: 15px;text-align: center\">[latex]3[\/latex]<\/td>\r\n<td style=\"height: 15px;text-align: center\">[latex]10.75[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"height: 15px;text-align: center\">[latex]4[\/latex]<\/td>\r\n<td style=\"height: 15px;text-align: center\">[latex]11.5[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"height: 15px;text-align: center\">[latex]5[\/latex]<\/td>\r\n<td style=\"height: 15px;text-align: center\">[latex]12.25[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"height: 15px;text-align: center\">[latex]6[\/latex]<\/td>\r\n<td style=\"height: 15px;text-align: center\">[latex]13[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThe data show that, yes, there are more commercials now than in [latex]2009[\/latex]. Joan decides the table is not very exciting because of the success she had with her manager when she reported her increase in sales using a graph.\u00a0Also, Devon\u00a0doubts that his readers will actually read a table. He agrees that a graph is\u00a0the perfect thing to post on his blog to convince his\u00a0skeptical readers!\r\n\r\nThey\u00a0get to work.\r\n\r\nFirst, they figure out what information they need to draw a graph of the line that represents the change in the number of minutes of commercials in one hour of TV since\u00a0[latex]2009[\/latex]?\r\n\r\nJoan\u00a0remembers that the coordinate plane\u00a0gives graphs structure and meaning. A straight line on a page will not tell Devon's\u00a0readers much. Joan\u00a0draws the axes and labels the horizontal one \"Years Since [latex]2009[\/latex],\" because that is the first data point they have. \u00a0Then Devon labels the vertical axis from\u00a0[latex]1[\/latex] to\u00a0[latex]18[\/latex], because the minute data ranges from\u00a0[latex]8.5[\/latex] to\u00a0[latex]13[\/latex] minutes.\r\n\r\n<img class=\"aligncenter wp-image-1433\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/03\/08193221\/Putting-It-Together-Graphing-1.png\" alt=\"A graph, with the y-axis representing the number of minutes of commercials in one hour of television and the x-axis representing years since 2009. The y-axis is numbered 0 through 18 by twos, and the x-axis is labeled 0 through 8 by ones.\" width=\"350\" height=\"269\" \/>\r\n\r\nThey plot the ordered pairs from the table of values on the\u00a0coordinate plane as shown below.\r\n\r\n<img class=\"aligncenter wp-image-1434\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/03\/08193353\/Putting-it-Together-Graphs-2.png\" alt=\"The previous graph, with added points: the point (0,8.5), the point (1, 9.25), the point (2,10), the point (3,10.75), the point (4,11.5), the point (5,12.25), and the point (6,13).\" width=\"350\" height=\"270\" \/>\r\n\r\nThe points\u00a0give them a guide for drawing the line which is shown below.\r\n\r\n<img class=\"aligncenter wp-image-1435\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/03\/08193449\/Putting-it-Together-3.png\" alt=\"An upward-sloping line drawn through the point (0,8.5), the point (1, 9.25), the point (2,10), the point (3,10.75), the point (4,11.5), the point (5,12.25), and the point (6,13).\" width=\"351\" height=\"270\" \/>\r\n\r\nDevon is excited to\u00a0post the graph on his\u00a0blog to\u00a0show people how much more time they are being exposed to commercials in one hour of watching TV.","rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignright wp-image-1475\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/03\/08220702\/2947716919_497a13c7ed_b.jpg\" alt=\"Watercolor painting\/sketch of a &quot;sad&quot; TV. On the screen is a simple frowny face.\" width=\"225\" height=\"225\" \/><\/p>\n<p>Joan&#8217;s uncle Devon is\u00a0a semiprofessional blogger who writes about media (he would really like to be a paid\u00a0film critic, but no one has offered yet). Recently, Devon posted a short blog piece complaining\u00a0about the number of ads on TV these days compared to\u00a0when he was younger. He was not very scientific about it, and a couple\u00a0of his\u00a0readers disputed a\u00a0claim he made and\u00a0tried to start an argument.<\/p>\n<p>Devon\u00a0asks\u00a0Joan, who is taking an algebra class at night, to\u00a0help him gather and cite some data to support his claim\u00a0that there are\u00a0&#8220;way more&#8221; TV ads now than when he was a kid. Together, they\u00a0get\u00a0online and do a little research and find a website that reports some interesting data on the number of minutes of TV commercials per hour since 2009. The data is shown below.<\/p>\n<table>\n<thead>\n<tr style=\"height: 15px\">\n<th style=\"height: 15px;text-align: center\">Years Since 2009<\/th>\n<th style=\"height: 15px;text-align: center\">Minutes<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr style=\"height: 15.5938px\">\n<td style=\"height: 15.5938px;text-align: center\">[latex]0[\/latex]<\/td>\n<td style=\"height: 15.5938px;text-align: center\">[latex]8.5[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px;text-align: center\">[latex]1[\/latex]<\/td>\n<td style=\"height: 15px;text-align: center\">[latex]9.25[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px;text-align: center\">[latex]2[\/latex]<\/td>\n<td style=\"height: 15px;text-align: center\">[latex]10[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px;text-align: center\">[latex]3[\/latex]<\/td>\n<td style=\"height: 15px;text-align: center\">[latex]10.75[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px;text-align: center\">[latex]4[\/latex]<\/td>\n<td style=\"height: 15px;text-align: center\">[latex]11.5[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px;text-align: center\">[latex]5[\/latex]<\/td>\n<td style=\"height: 15px;text-align: center\">[latex]12.25[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px;text-align: center\">[latex]6[\/latex]<\/td>\n<td style=\"height: 15px;text-align: center\">[latex]13[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>The data show that, yes, there are more commercials now than in [latex]2009[\/latex]. Joan decides the table is not very exciting because of the success she had with her manager when she reported her increase in sales using a graph.\u00a0Also, Devon\u00a0doubts that his readers will actually read a table. He agrees that a graph is\u00a0the perfect thing to post on his blog to convince his\u00a0skeptical readers!<\/p>\n<p>They\u00a0get to work.<\/p>\n<p>First, they figure out what information they need to draw a graph of the line that represents the change in the number of minutes of commercials in one hour of TV since\u00a0[latex]2009[\/latex]?<\/p>\n<p>Joan\u00a0remembers that the coordinate plane\u00a0gives graphs structure and meaning. A straight line on a page will not tell Devon&#8217;s\u00a0readers much. Joan\u00a0draws the axes and labels the horizontal one &#8220;Years Since [latex]2009[\/latex],&#8221; because that is the first data point they have. \u00a0Then Devon labels the vertical axis from\u00a0[latex]1[\/latex] to\u00a0[latex]18[\/latex], because the minute data ranges from\u00a0[latex]8.5[\/latex] to\u00a0[latex]13[\/latex] minutes.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1433\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/03\/08193221\/Putting-It-Together-Graphing-1.png\" alt=\"A graph, with the y-axis representing the number of minutes of commercials in one hour of television and the x-axis representing years since 2009. The y-axis is numbered 0 through 18 by twos, and the x-axis is labeled 0 through 8 by ones.\" width=\"350\" height=\"269\" \/><\/p>\n<p>They plot the ordered pairs from the table of values on the\u00a0coordinate plane as shown below.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1434\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/03\/08193353\/Putting-it-Together-Graphs-2.png\" alt=\"The previous graph, with added points: the point (0,8.5), the point (1, 9.25), the point (2,10), the point (3,10.75), the point (4,11.5), the point (5,12.25), and the point (6,13).\" width=\"350\" height=\"270\" \/><\/p>\n<p>The points\u00a0give them a guide for drawing the line which is shown below.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1435\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/03\/08193449\/Putting-it-Together-3.png\" alt=\"An upward-sloping line drawn through the point (0,8.5), the point (1, 9.25), the point (2,10), the point (3,10.75), the point (4,11.5), the point (5,12.25), and the point (6,13).\" width=\"351\" height=\"270\" \/><\/p>\n<p>Devon is excited to\u00a0post the graph on his\u00a0blog to\u00a0show people how much more time they are being exposed to commercials in one hour of watching TV.<\/p>\n","protected":false},"author":21,"menu_order":8,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"b186eb84-a25f-4832-aee7-8a1cec3c6e2c","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1783","chapter","type-chapter","status-publish","hentry"],"part":473,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters\/1783","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/wp\/v2\/users\/21"}],"version-history":[{"count":12,"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters\/1783\/revisions"}],"predecessor-version":[{"id":4929,"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters\/1783\/revisions\/4929"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/pressbooks\/v2\/parts\/473"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters\/1783\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/wp\/v2\/media?parent=1783"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=1783"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/wp\/v2\/contributor?post=1783"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/wp\/v2\/license?post=1783"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}