{"id":4654,"date":"2017-06-07T18:54:12","date_gmt":"2017-06-07T18:54:12","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/chapter\/read-interpreting-slope-in-equations-and-graphs\/"},"modified":"2017-08-16T03:20:11","modified_gmt":"2017-08-16T03:20:11","slug":"read-interpreting-slope-in-equations-and-graphs","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/chapter\/read-interpreting-slope-in-equations-and-graphs\/","title":{"raw":"Applications: Interpreting Slope in Equations and Graphs","rendered":"Applications: Interpreting Slope in Equations and Graphs"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\">\r\n<h3>Learning Objectives<\/h3>\r\n<ul>\r\n \t<li>Interpret slope in equations and graphs\r\n<ul>\r\n \t<li>Verify the slope of a linear equation given a dataset<\/li>\r\n \t<li>Interpret the slope of a linear equation as it applies to a real situation<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Verify Slope From a Dataset<\/h2>\r\nMassive amounts of data is being collected every day by a wide range of institutions and groups. \u00a0This data is used for many purposes including business decisions about location and marketing, government decisions about allocation of resources and infrastructure, and personal decisions about where to live or where to buy food.\r\n\r\nIn the following example, you will see how a dataset can be used to define\u00a0the slope of a linear equation.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nGiven the dataset, verify the values of the slopes of each equation.\r\n\r\nLinear equations describing the change in median home values between 1950 and 2000 in Mississippi and Hawaii are as follows:\r\n\r\n<strong>Hawaii:\u00a0<\/strong> [latex]y=3966x+74,400[\/latex]\r\n\r\n<strong>Mississippi:\u00a0\u00a0<\/strong>[latex]y=924x+25,200[\/latex]\r\n\r\nThe equations are based on the following dataset.\r\n\r\nx = the number of years since 1950, and y = the median value of a house in the given state.\r\n<table id=\"Table_04_02_03\" summary=\"This table shows three rows and three columns. The first column is labeled: \u201cYear\u201d, the second: \u201cMississippi\u201d and the third: \u201cHawaii\u201d. The two year entries are: \u201c1950\u201d and \u201c2000\u201d. The two Mississippi entries are: \u201c$25,200\u201d and \u201c$71,400\u201d. The two Hawaii entries are: \u201c$74,400\u201d and \u201c$272,700\u201d.\">\r\n<thead>\r\n<tr>\r\n<th scope=\"col\">Year (<em>x<\/em>)<\/th>\r\n<th scope=\"col\">Mississippi House Value (<em>y<\/em>)<\/th>\r\n<th scope=\"col\">Hawaii House Value (<em>y<\/em>)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>0<\/td>\r\n<td>$25,200<\/td>\r\n<td>$74,400<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>50<\/td>\r\n<td>$71,400<\/td>\r\n<td>$272,700<strong>\u00a0\u00a0<\/strong><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThe slopes of each equation can be calculated with the formula you learned in the section on slope.\r\n<p style=\"text-align: center\">[latex] \\displaystyle m=\\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}[\/latex]<\/p>\r\n<strong>Mississippi:<\/strong>\r\n<table>\r\n<thead>\r\n<tr>\r\n<th>Name<\/th>\r\n<th>Ordered Pair<\/th>\r\n<th>Coordinates<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>Point 1<\/td>\r\n<td>(0, 25,200)<\/td>\r\n<td>[latex]\\begin{array}{l}x_{1}=0\\\\y_{1}=25,200\\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Point 2<\/td>\r\n<td>(50, 71,400)<\/td>\r\n<td>[latex]\\begin{array}{l}x_{2}=50\\\\y_{2}=71,400\\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p style=\"text-align: center\">[latex] \\displaystyle m=\\frac{{71,400}-{25,200}}{{50}-{0}}=\\frac{{46,200}}{{50}} = 924[\/latex]<\/p>\r\nWe have verified that the slope [latex] \\displaystyle m = 924[\/latex] matches the dataset provided.\r\n\r\n<strong>Hawaii:<\/strong>\r\n<table>\r\n<thead>\r\n<tr>\r\n<th>Name<\/th>\r\n<th>Ordered Pair<\/th>\r\n<th>Coordinates<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>Point 1<\/td>\r\n<td>(0, 74,400)<\/td>\r\n<td>[latex]\\begin{array}{l}x_{1}=1950\\\\y_{1}=74,400\\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Point 2<\/td>\r\n<td>(50, 272,700)<\/td>\r\n<td>[latex]\\begin{array}{l}x_{2}=2000\\\\y_{2}=272,700\\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p style=\"text-align: center\">[latex]\\displaystyle m=\\frac{{272,700}-{74,400}}{{50}-{0}}=\\frac{{198,300}}{{50}} = 3966[\/latex]<\/p>\r\nWe have verified that the slope [latex] \\displaystyle m = 3966[\/latex] matches the dataset provided.\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nGiven the dataset, verify the values of the slopes of the\u00a0equation.\r\n\r\nA linear equation describing the change in the number of high school students who smoke, in\u00a0a group of 100, between 2011 and 2015 is given as:\r\n<p style=\"text-align: center\">\u00a0[latex]y = -1.75x+16[\/latex]<\/p>\r\nAnd is based on the data from this table, provided by the Centers for Disease Control.\r\n\r\nx = the number of years since 2011, and y = the number of high school smokers per 100 students.\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td>Year<\/td>\r\n<td>Number of \u00a0High School Students Smoking\u00a0Cigarettes (per 100)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>0<\/td>\r\n<td>16<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>4<\/td>\r\n<td>9<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table>\r\n<thead>\r\n<tr>\r\n<th>Name<\/th>\r\n<th>Ordered Pair<\/th>\r\n<th>Coordinates<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>Point 1<\/td>\r\n<td>(0, 16)<\/td>\r\n<td>[latex]\\begin{array}{l}x_{1}=0\\\\y_{1}=16\\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Point 2<\/td>\r\n<td>(4, 9)<\/td>\r\n<td>[latex]\\begin{array}{l}x_{2}=4\\\\y_{2}=9\\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p style=\"text-align: center\">[latex] \\displaystyle m=\\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}=\\frac{{9-16}}{{4-0}} =\\frac{{-7}}{{4}}=-1.75[\/latex]<\/p>\r\nWe have verified that the slope [latex] \\displaystyle{m=-1.75}[\/latex] matches the dataset provided.\r\n\r\n<\/div>\r\n<h2>Interpret the Slope of \u00a0Linear Equation<\/h2>\r\nOkay, now we have verified that data can provide us with the slope of a linear equation. So what? We can use this information to describe how something changes using words.\r\n\r\nFirst, let's review the different kinds of slopes possible in a linear equation.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2011\/2017\/06\/07185356\/image042.gif\" alt=\"Uphill line with positive slope has a line that starts at the bottom-left and goes into the top-right of the graph. Downhill line with negative slope starts in the top-left and ends in the bottom-right part of the graph. Horizontal lines have a slope of 0. Vertical lines have an undefined slope.\" width=\"456\" height=\"183\" \/>\r\n\r\nWe often use specific words to describe the different types of slopes when we are using lines and equations to represent \"real\" situations. The following table pairs the type of slope with the common language used to describe it both verbally and visually.\r\n<table style=\"height: 145px;width: 533px\">\r\n<tbody>\r\n<tr>\r\n<td><strong>Type of Slope<\/strong><\/td>\r\n<td><strong>Visual Description\u00a0<\/strong><\/td>\r\n<td><strong>Verbal Description<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>positive<\/td>\r\n<td>uphill<\/td>\r\n<td>increasing<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>negative<\/td>\r\n<td>downhill<\/td>\r\n<td>decreasing<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>0<\/td>\r\n<td>horizontal<\/td>\r\n<td>constant<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>undefined<\/td>\r\n<td>vertical<\/td>\r\n<td>N\/A<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nInterpret the slope of each equation for house values using words.\r\n\r\n<strong>Hawaii:\u00a0<\/strong> [latex]y = 3966x+74,400[\/latex]\r\n\r\n<strong>Mississippi:\u00a0\u00a0<\/strong>[latex]y = 924x+25,200[\/latex]\r\n\r\n[reveal-answer q=\"871726\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"871726\"]It helps to apply the units to the points that we used to define slope. \u00a0The <em>x<\/em>-values represent years, and the <em>y<\/em>-values represent dollar amounts.\r\n\r\nFor Mississippi:\r\n<p style=\"text-align: center\">[latex] \\displaystyle m=\\frac{{71,400}-{25,200}}{{0}-{50}}=\\frac{{46,200\\text{ dollars}}}{{50\\text{ year}}} = 924\\frac{\\text{dollars}}{\\text{year}}[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\nThe slope for the Mississippi home prices equation is <strong>positive<\/strong>, so each year the price of a home in Mississippi\u00a0<strong>increases<\/strong> by 924 dollars.\r\n\r\nWe can apply the same thinking for Hawaii home prices. The slope for the Hawaii\u00a0home prices equation tells us that each year, the price of a home increases by 3966\u00a0dollars.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<h2 class=\"yt watch-title-container\"><span class=\"watch-title\" dir=\"ltr\" title=\"Intepret the Meaning of the Slope Given a Linear Equation - Median Home Values\">Interpret the Meaning of the Slope Given a Linear Equation\u2014Median Home Values<\/span><\/h2>\r\nhttps:\/\/youtu.be\/JT0WX5KOkJ8\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nInterpret the slope of the line describing the change in the number of high school smokers using words.\r\n\r\nApply units to the formula for slope. The <em>x<\/em> values represent years, and the <em>y<\/em> values represent the number of smokers. Remember that this dataset is per 100 high school students.\r\n<p style=\"text-align: center\">[latex] \\displaystyle m=\\frac{{9-16}}{{2015-2011}} =\\frac{{-7 \\text{ smokers}}}{{4\\text{ year}}}=-1.75\\frac{\\text{ smokers}}{\\text{ year}}[\/latex]<\/p>\r\nThe slope of this linear equation is <strong>negative<\/strong>, so this tells us that there is a <strong>decrease<\/strong> in the number of high school age smokers each year.\r\n\r\nThe number of high schoolers that smoke decreases by 1.75 per 100 each year.\r\n\r\n<\/div>\r\n<h2>Interpret the Meaning of the Slope of a Linear Equation\u2014Smokers<\/h2>\r\nhttps:\/\/youtu.be\/aHLw5FcMjdc\r\n\r\nOn the next page, we will see how to interpret the <em>y<\/em>-intercept of a linear equation, and make a prediction based on a linear equation.","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Objectives<\/h3>\n<ul>\n<li>Interpret slope in equations and graphs\n<ul>\n<li>Verify the slope of a linear equation given a dataset<\/li>\n<li>Interpret the slope of a linear equation as it applies to a real situation<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/div>\n<h2>Verify Slope From a Dataset<\/h2>\n<p>Massive amounts of data is being collected every day by a wide range of institutions and groups. \u00a0This data is used for many purposes including business decisions about location and marketing, government decisions about allocation of resources and infrastructure, and personal decisions about where to live or where to buy food.<\/p>\n<p>In the following example, you will see how a dataset can be used to define\u00a0the slope of a linear equation.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Given the dataset, verify the values of the slopes of each equation.<\/p>\n<p>Linear equations describing the change in median home values between 1950 and 2000 in Mississippi and Hawaii are as follows:<\/p>\n<p><strong>Hawaii:\u00a0<\/strong> [latex]y=3966x+74,400[\/latex]<\/p>\n<p><strong>Mississippi:\u00a0\u00a0<\/strong>[latex]y=924x+25,200[\/latex]<\/p>\n<p>The equations are based on the following dataset.<\/p>\n<p>x = the number of years since 1950, and y = the median value of a house in the given state.<\/p>\n<table id=\"Table_04_02_03\" summary=\"This table shows three rows and three columns. The first column is labeled: \u201cYear\u201d, the second: \u201cMississippi\u201d and the third: \u201cHawaii\u201d. The two year entries are: \u201c1950\u201d and \u201c2000\u201d. The two Mississippi entries are: \u201c$25,200\u201d and \u201c$71,400\u201d. The two Hawaii entries are: \u201c$74,400\u201d and \u201c$272,700\u201d.\">\n<thead>\n<tr>\n<th scope=\"col\">Year (<em>x<\/em>)<\/th>\n<th scope=\"col\">Mississippi House Value (<em>y<\/em>)<\/th>\n<th scope=\"col\">Hawaii House Value (<em>y<\/em>)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>0<\/td>\n<td>$25,200<\/td>\n<td>$74,400<\/td>\n<\/tr>\n<tr>\n<td>50<\/td>\n<td>$71,400<\/td>\n<td>$272,700<strong>\u00a0\u00a0<\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>The slopes of each equation can be calculated with the formula you learned in the section on slope.<\/p>\n<p style=\"text-align: center\">[latex]\\displaystyle m=\\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}[\/latex]<\/p>\n<p><strong>Mississippi:<\/strong><\/p>\n<table>\n<thead>\n<tr>\n<th>Name<\/th>\n<th>Ordered Pair<\/th>\n<th>Coordinates<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Point 1<\/td>\n<td>(0, 25,200)<\/td>\n<td>[latex]\\begin{array}{l}x_{1}=0\\\\y_{1}=25,200\\end{array}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Point 2<\/td>\n<td>(50, 71,400)<\/td>\n<td>[latex]\\begin{array}{l}x_{2}=50\\\\y_{2}=71,400\\end{array}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: center\">[latex]\\displaystyle m=\\frac{{71,400}-{25,200}}{{50}-{0}}=\\frac{{46,200}}{{50}} = 924[\/latex]<\/p>\n<p>We have verified that the slope [latex]\\displaystyle m = 924[\/latex] matches the dataset provided.<\/p>\n<p><strong>Hawaii:<\/strong><\/p>\n<table>\n<thead>\n<tr>\n<th>Name<\/th>\n<th>Ordered Pair<\/th>\n<th>Coordinates<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Point 1<\/td>\n<td>(0, 74,400)<\/td>\n<td>[latex]\\begin{array}{l}x_{1}=1950\\\\y_{1}=74,400\\end{array}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Point 2<\/td>\n<td>(50, 272,700)<\/td>\n<td>[latex]\\begin{array}{l}x_{2}=2000\\\\y_{2}=272,700\\end{array}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: center\">[latex]\\displaystyle m=\\frac{{272,700}-{74,400}}{{50}-{0}}=\\frac{{198,300}}{{50}} = 3966[\/latex]<\/p>\n<p>We have verified that the slope [latex]\\displaystyle m = 3966[\/latex] matches the dataset provided.<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Given the dataset, verify the values of the slopes of the\u00a0equation.<\/p>\n<p>A linear equation describing the change in the number of high school students who smoke, in\u00a0a group of 100, between 2011 and 2015 is given as:<\/p>\n<p style=\"text-align: center\">\u00a0[latex]y = -1.75x+16[\/latex]<\/p>\n<p>And is based on the data from this table, provided by the Centers for Disease Control.<\/p>\n<p>x = the number of years since 2011, and y = the number of high school smokers per 100 students.<\/p>\n<table>\n<tbody>\n<tr>\n<td>Year<\/td>\n<td>Number of \u00a0High School Students Smoking\u00a0Cigarettes (per 100)<\/td>\n<\/tr>\n<tr>\n<td>0<\/td>\n<td>16<\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td>9<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table>\n<thead>\n<tr>\n<th>Name<\/th>\n<th>Ordered Pair<\/th>\n<th>Coordinates<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Point 1<\/td>\n<td>(0, 16)<\/td>\n<td>[latex]\\begin{array}{l}x_{1}=0\\\\y_{1}=16\\end{array}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Point 2<\/td>\n<td>(4, 9)<\/td>\n<td>[latex]\\begin{array}{l}x_{2}=4\\\\y_{2}=9\\end{array}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: center\">[latex]\\displaystyle m=\\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}=\\frac{{9-16}}{{4-0}} =\\frac{{-7}}{{4}}=-1.75[\/latex]<\/p>\n<p>We have verified that the slope [latex]\\displaystyle{m=-1.75}[\/latex] matches the dataset provided.<\/p>\n<\/div>\n<h2>Interpret the Slope of \u00a0Linear Equation<\/h2>\n<p>Okay, now we have verified that data can provide us with the slope of a linear equation. So what? We can use this information to describe how something changes using words.<\/p>\n<p>First, let&#8217;s review the different kinds of slopes possible in a linear equation.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2011\/2017\/06\/07185356\/image042.gif\" alt=\"Uphill line with positive slope has a line that starts at the bottom-left and goes into the top-right of the graph. Downhill line with negative slope starts in the top-left and ends in the bottom-right part of the graph. Horizontal lines have a slope of 0. Vertical lines have an undefined slope.\" width=\"456\" height=\"183\" \/><\/p>\n<p>We often use specific words to describe the different types of slopes when we are using lines and equations to represent &#8220;real&#8221; situations. The following table pairs the type of slope with the common language used to describe it both verbally and visually.<\/p>\n<table style=\"height: 145px;width: 533px\">\n<tbody>\n<tr>\n<td><strong>Type of Slope<\/strong><\/td>\n<td><strong>Visual Description\u00a0<\/strong><\/td>\n<td><strong>Verbal Description<\/strong><\/td>\n<\/tr>\n<tr>\n<td>positive<\/td>\n<td>uphill<\/td>\n<td>increasing<\/td>\n<\/tr>\n<tr>\n<td>negative<\/td>\n<td>downhill<\/td>\n<td>decreasing<\/td>\n<\/tr>\n<tr>\n<td>0<\/td>\n<td>horizontal<\/td>\n<td>constant<\/td>\n<\/tr>\n<tr>\n<td>undefined<\/td>\n<td>vertical<\/td>\n<td>N\/A<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Interpret the slope of each equation for house values using words.<\/p>\n<p><strong>Hawaii:\u00a0<\/strong> [latex]y = 3966x+74,400[\/latex]<\/p>\n<p><strong>Mississippi:\u00a0\u00a0<\/strong>[latex]y = 924x+25,200[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q871726\">Show Solution<\/span><\/p>\n<div id=\"q871726\" class=\"hidden-answer\" style=\"display: none\">It helps to apply the units to the points that we used to define slope. \u00a0The <em>x<\/em>-values represent years, and the <em>y<\/em>-values represent dollar amounts.<\/p>\n<p>For Mississippi:<\/p>\n<p style=\"text-align: center\">[latex]\\displaystyle m=\\frac{{71,400}-{25,200}}{{0}-{50}}=\\frac{{46,200\\text{ dollars}}}{{50\\text{ year}}} = 924\\frac{\\text{dollars}}{\\text{year}}[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>The slope for the Mississippi home prices equation is <strong>positive<\/strong>, so each year the price of a home in Mississippi\u00a0<strong>increases<\/strong> by 924 dollars.<\/p>\n<p>We can apply the same thinking for Hawaii home prices. The slope for the Hawaii\u00a0home prices equation tells us that each year, the price of a home increases by 3966\u00a0dollars.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<h2 class=\"yt watch-title-container\"><span class=\"watch-title\" dir=\"ltr\" title=\"Intepret the Meaning of the Slope Given a Linear Equation - Median Home Values\">Interpret the Meaning of the Slope Given a Linear Equation\u2014Median Home Values<\/span><\/h2>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Interpret the Meaning of the Slope Given a Linear Equation - Median Home Values\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/JT0WX5KOkJ8?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Interpret the slope of the line describing the change in the number of high school smokers using words.<\/p>\n<p>Apply units to the formula for slope. The <em>x<\/em> values represent years, and the <em>y<\/em> values represent the number of smokers. Remember that this dataset is per 100 high school students.<\/p>\n<p style=\"text-align: center\">[latex]\\displaystyle m=\\frac{{9-16}}{{2015-2011}} =\\frac{{-7 \\text{ smokers}}}{{4\\text{ year}}}=-1.75\\frac{\\text{ smokers}}{\\text{ year}}[\/latex]<\/p>\n<p>The slope of this linear equation is <strong>negative<\/strong>, so this tells us that there is a <strong>decrease<\/strong> in the number of high school age smokers each year.<\/p>\n<p>The number of high schoolers that smoke decreases by 1.75 per 100 each year.<\/p>\n<\/div>\n<h2>Interpret the Meaning of the Slope of a Linear Equation\u2014Smokers<\/h2>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Interpret the Meaning of the Slope of a Linear Equation - Smokers\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/aHLw5FcMjdc?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>On the next page, we will see how to interpret the <em>y<\/em>-intercept of a linear equation, and make a prediction based on a linear equation.<\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-4654\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Intepret the Meaning of the Slope Given a Linear Equation - Median Home Values. <strong>Authored by<\/strong>: Mathispower4u. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/JT0WX5KOkJ8\">https:\/\/youtu.be\/JT0WX5KOkJ8<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/pdm\">Public Domain: No Known Copyright<\/a><\/em><\/li><li>Intepret the Meaning of the Slope of a Linear Equation - Smokers. <strong>Authored by<\/strong>: Mathispower4u. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/aHLw5FcMjdc\">https:\/\/youtu.be\/aHLw5FcMjdc<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/pdm\">Public Domain: No Known Copyright<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">Public domain content<\/div><ul class=\"citation-list\"><li>Youth and Tobacco Use. <strong>Authored by<\/strong>: Centers for Disease Control and Prevention. <strong>Provided by<\/strong>: U.S. Department of Health and Human Services. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/www.cdc.gov\/tobacco\/data_statistics\/fact_sheets\/youth_data\/tobacco_use\/index.htm\">http:\/\/www.cdc.gov\/tobacco\/data_statistics\/fact_sheets\/youth_data\/tobacco_use\/index.htm<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/pdm\">Public Domain: No Known Copyright<\/a><\/em><\/li><li>Historical Census of Housing Tables Home Values. <strong>Authored by<\/strong>: United States Census Bureau. <strong>Provided by<\/strong>: U.S. Dept. of Housing. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/www.census.gov\/hhes\/www\/housing\/census\/historic\/values.html\">https:\/\/www.census.gov\/hhes\/www\/housing\/census\/historic\/values.html<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/pdm\">Public Domain: No Known Copyright<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":17533,"menu_order":12,"template":"","meta":{"_candela_citation":"[{\"type\":\"pd\",\"description\":\"Youth and Tobacco Use\",\"author\":\"Centers for Disease Control and Prevention\",\"organization\":\"U.S. Department of Health and Human Services\",\"url\":\"http:\/\/www.cdc.gov\/tobacco\/data_statistics\/fact_sheets\/youth_data\/tobacco_use\/index.htm\",\"project\":\"\",\"license\":\"pd\",\"license_terms\":\"\"},{\"type\":\"pd\",\"description\":\"Historical Census of Housing Tables Home Values\",\"author\":\"United States Census Bureau\",\"organization\":\"U.S. Dept. of Housing\",\"url\":\"https:\/\/www.census.gov\/hhes\/www\/housing\/census\/historic\/values.html\",\"project\":\"\",\"license\":\"pd\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Intepret the Meaning of the Slope Given a Linear Equation - 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