{"id":5027,"date":"2016-07-20T21:05:58","date_gmt":"2016-07-20T21:05:58","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/microeconomics\/?post_type=chapter&p=5027"},"modified":"2016-07-20T21:05:58","modified_gmt":"2016-07-20T21:05:58","slug":"reading-creating-and-interpreting-graphs","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/atd-herkimer-microeconomics\/chapter\/reading-creating-and-interpreting-graphs\/","title":{"raw":"Reading: Creating and Interpreting Graphs","rendered":"Reading: Creating and Interpreting Graphs"},"content":{"raw":"
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\n\nIt\u2019s important to know\u00a0the terminology of graphs in order to understand and manipulate them. Let\u2019s begin with a visual representation of the terms (shown in Figure 1), and then we can discuss each one in greater detail.\n
\n\n[caption id=\"attachment_6788\" align=\"aligncenter\" width=\"501\"]\"A<\/a> Figure 1. Graph Terminology<\/strong>[\/caption]\n\n<\/div>\nThroughout this course we will refer to the horizontal line on the graph as the x-axis<\/strong>. We will refer to the vertical line on the graph as the\u00a0y-axis<\/strong>. This is the standard\u00a0convention for graphs.\n\nAn\u00a0intercept<\/strong> is where a line on a graph crosses (\"intercepts\") the x-axis or the y-axis. You can see the x-intercepts and y-intercepts on the graph above. The point where two lines on a graph cross is called the\u00a0interception point<\/strong>.\n\nThe other important term to know\u00a0is slope<\/em>. The slope tells us how steep a line on a graph is. Technically, slope<\/strong> is the change in the vertical axis divided by the change in the horizontal axis. The formula for calculating the slope is often referred to as the \u201crise over the run\u201d\u2014again, the change in the distance on the y-axis (rise) divided by the change in the x-axis (run).\n\n<\/div>\n<\/div>\nNow that you know the \"parts\" of a graph,\u00a0let's turn to\u00a0the equation for a line:\n
\n
y\u00a0= b\u00a0+ mx<\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n<\/div>\nLet's\u00a0use the same equation\u00a0we used\u00a0earlier, in the\u00a0section on solving algebraic equations:\n

y = 9 + 3x<\/p>\nIn this equation for a line, the b<\/em> term is\u00a09 and the m<\/em> term is\u00a03. The table below\u00a0shows the\u00a0values of x<\/em> and y<\/em> for this equation.\u00a0To construct the table, just plug in a series of different values for x<\/em>, and then calculate the resulting values for\u00a0y<\/em>.<\/span>\n
Values for the Slope Intercept Equation<\/span><\/caption>\n
x<\/th>\ny<\/th>\n<\/tr><\/thead>
0<\/td>\n9<\/td>\n<\/tr>
1<\/td>\n12<\/td>\n<\/tr>
2<\/td>\n15<\/td>\n<\/tr>
3<\/td>\n18<\/td>\n<\/tr>
4<\/td>\n21<\/td>\n<\/tr>
5<\/td>\n24<\/td>\n<\/tr>
6<\/td>\n27<\/td>\n<\/tr><\/tbody><\/table>
Next we can place\u00a0each of these points on a graph. We can start with 0 on the x<\/em>-axis and plot a point at 9 on the y<\/em>-axis. We can do the same with the other pairs of values and draw a line through all the points, as on the graph in Figure 2, below.<\/div>\n
\n\n[caption id=\"\" align=\"aligncenter\" width=\"501\"]\"TheFigure 2. Slope and Algebra of a Straight Line<\/strong>[\/caption]\n\n<\/figure>

This example illustrates how the b<\/em> and m<\/em> terms in an equation for a straight line determine the shape of the line. The b<\/em> term is called the y<\/em>-intercept. The reason is that if x<\/em> = 0, the b<\/em> term will reveal where the line intercepts, or crosses, the y<\/em>-axis. In this example, the line hits the vertical axis at 9. The m<\/em> term in the equation for the line is the slope. Remember that slope<\/span> is defined as rise over run; the slope of a line from one point to another is the change in the vertical axis divided by the change in the horizontal axis. In this example, each time the x<\/em> term increases by 1\u00a0(the run), the y<\/em> term rises by 3. Thus, the slope of this line is 3. Specifying a y<\/em>-intercept and a slope\u2014that is, specifying b<\/em> and m<\/em> in the equation for a line\u2014will identify a specific line. Although it is rare for real-world data points to arrange themselves as a perfectly\u00a0straight line, it often turns out that a straight line can offer a reasonable approximation of actual data.<\/p>","rendered":"

\n
\n

It\u2019s important to know\u00a0the terminology of graphs in order to understand and manipulate them. Let\u2019s begin with a visual representation of the terms (shown in Figure 1), and then we can discuss each one in greater detail.<\/p>\n

\n
\"A<\/a><\/p>\n

Figure 1. Graph Terminology<\/strong><\/p>\n<\/div>\n<\/div>\n

Throughout this course we will refer to the horizontal line on the graph as the x-axis<\/strong>. We will refer to the vertical line on the graph as the\u00a0y-axis<\/strong>. This is the standard\u00a0convention for graphs.<\/p>\n

An\u00a0intercept<\/strong> is where a line on a graph crosses (“intercepts”) the x-axis or the y-axis. You can see the x-intercepts and y-intercepts on the graph above. The point where two lines on a graph cross is called the\u00a0interception point<\/strong>.<\/p>\n

The other important term to know\u00a0is slope<\/em>. The slope tells us how steep a line on a graph is. Technically, slope<\/strong> is the change in the vertical axis divided by the change in the horizontal axis. The formula for calculating the slope is often referred to as the \u201crise over the run\u201d\u2014again, the change in the distance on the y-axis (rise) divided by the change in the x-axis (run).<\/p>\n<\/div>\n<\/div>\n

Now that you know the “parts” of a graph,\u00a0let’s turn to\u00a0the equation for a line:<\/p>\n

\n
y\u00a0= b\u00a0+ mx<\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n<\/div>\n

Let’s\u00a0use the same equation\u00a0we used\u00a0earlier, in the\u00a0section on solving algebraic equations:<\/p>\n

y = 9 + 3x<\/p>\n

In this equation for a line, the b<\/em> term is\u00a09 and the m<\/em> term is\u00a03. The table below\u00a0shows the\u00a0values of x<\/em> and y<\/em> for this equation.\u00a0To construct the table, just plug in a series of different values for x<\/em>, and then calculate the resulting values for\u00a0y<\/em>.<\/span><\/p>\n\n\n\n\n\n\n\n\n\n\n\n
Values for the Slope Intercept Equation<\/span><\/caption>\n
x<\/th>\ny<\/th>\n<\/tr>\n<\/thead>\n
0<\/td>\n9<\/td>\n<\/tr>\n
1<\/td>\n12<\/td>\n<\/tr>\n
2<\/td>\n15<\/td>\n<\/tr>\n
3<\/td>\n18<\/td>\n<\/tr>\n
4<\/td>\n21<\/td>\n<\/tr>\n
5<\/td>\n24<\/td>\n<\/tr>\n
6<\/td>\n27<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
Next we can place\u00a0each of these points on a graph. We can start with 0 on the x<\/em>-axis and plot a point at 9 on the y<\/em>-axis. We can do the same with the other pairs of values and draw a line through all the points, as on the graph in Figure 2, below.<\/div>\n
\n
\"The<\/p>\n

Figure 2. Slope and Algebra of a Straight Line<\/strong><\/p>\n<\/div>\n<\/figure>\n

This example illustrates how the b<\/em> and m<\/em> terms in an equation for a straight line determine the shape of the line. The b<\/em> term is called the y<\/em>-intercept. The reason is that if x<\/em> = 0, the b<\/em> term will reveal where the line intercepts, or crosses, the y<\/em>-axis. In this example, the line hits the vertical axis at 9. The m<\/em> term in the equation for the line is the slope. Remember that slope<\/span> is defined as rise over run; the slope of a line from one point to another is the change in the vertical axis divided by the change in the horizontal axis. In this example, each time the x<\/em> term increases by 1\u00a0(the run), the y<\/em> term rises by 3. Thus, the slope of this line is 3. Specifying a y<\/em>-intercept and a slope\u2014that is, specifying b<\/em> and m<\/em> in the equation for a line\u2014will identify a specific line. Although it is rare for real-world data points to arrange themselves as a perfectly\u00a0straight line, it often turns out that a straight line can offer a reasonable approximation of actual data.<\/p>\n\n\t\t\t

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Candela Citations<\/h3>\n\t\t\t\t\t
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CC licensed content, Original<\/div>