{"id":5797,"date":"2016-07-19T18:01:55","date_gmt":"2016-07-19T18:01:55","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/macroeconomics\/?post_type=chapter&p=5797"},"modified":"2016-07-19T18:01:55","modified_gmt":"2016-07-19T18:01:55","slug":"reading-interpreting-slope","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-hccc-macroeconomics\/chapter\/reading-interpreting-slope\/","title":{"raw":"Reading: Interpreting Slope","rendered":"Reading: Interpreting Slope"},"content":{"raw":"

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

What the\u00a0Slope Means<\/strong><\/h2>\n

The concept of slope is very useful in economics, because it measures the relationship between two variables. A positive slope<\/strong>\u00a0<\/span>means that two variables are positively related\u2014that is, when x<\/em> increases, so does y<\/em>, and when x<\/em> decreases, y<\/em> decreases also. Graphically, a positive slope means that as a line on the line graph moves from left to right, the line rises. \u00a0We will learn in other sections\u00a0that \"price\" and \"quantity supplied\" have a positive relationship; that is, firms will supply more when the price is higher.<\/p>\n\n\n[caption id=\"attachment_6317\" align=\"aligncenter\" width=\"500\"]\"AFigure 1. Positive Slope<\/strong>[\/caption]\n

A negative slope<\/span><\/strong> means that two variables are negatively related; that is, when x<\/em> increases, y<\/em> decreases, and when x<\/em> decreases, y<\/em> increases. Graphically, a negative slope means that as the line on the line graph moves from left to right, the line falls. \u00a0We will learn that \"price\" and \"quantity demanded\" have a negative relationship; that is, consumers will purchase less when the price is higher.<\/p>\n\n\n[caption id=\"attachment_6320\" align=\"aligncenter\" width=\"500\"]\"AFigure 2. Negative slope<\/strong>[\/caption]\n

A slope of zero<\/strong> means that there is a constant\u00a0relationship between x<\/em> and y<\/em>. Graphically, the line is flat; the rise over run is zero.<\/p>\n\n\n[caption id=\"attachment_6321\" align=\"aligncenter\" width=\"500\"]\"AFigure 3. Slope of Zero<\/strong>[\/caption]\n\nThe unemployment-rate graph in Figure 4, below, illustrates a common pattern of many line graphs: some segments where the slope is positive, other segments where the slope is negative, and still other segments where the slope is close to zero.\n\n

\n\n[caption id=\"\" align=\"aligncenter\" width=\"500\"]\"TheFigure 4. U.S. Unemployment Rate, 1975\u20132014<\/strong>[\/caption]\n\n<\/figure>

Calculating Slope<\/h2>\n

The slope of a straight line between two points can be calculated in numerical terms. To calculate slope, begin by designating one point as the \u201cstarting point\u201d and the other point as the \u201cend point\u201d and then calculating the rise over run between these two points.<\/p>\n\n\n[caption id=\"\" align=\"aligncenter\" width=\"500\"]\"TheFigure 5. Altitude\u2013Air Density Relationship<\/strong>[\/caption]\n\nAs an example, consider the slope of the air-density graph, above, between the points representing an altitude of 4,000 meters and an altitude of 6,000 meters:\n

Rise: Change in variable on vertical axis (end point minus original point)<\/p>\n\n

\n
0.100\u00a0\u2013\u00a00.307\u00a0=\u00a0\u20130.207<\/span><\/span><\/div>\n<\/div>\n

Run: Change in variable on horizontal axis (end point minus original point)<\/p>\n\n

\n
6,000\u00a0\u2013\u00a04,000=\u00a02,000<\/span><\/span><\/div>\n<\/div>\n

Thus, the slope of a straight line between these two points would be the following: from the altitude of 4,000 meters up to 6,000 meters, the density of the air decreases by approximately 0.1 kilograms\/cubic meter for each of the next 1,000 meters.<\/p>\n

Suppose the slope of a line were to increase. Graphically, that means it would get steeper. Suppose the slope of a line were to decrease. Then it would get flatter. These conditions are true whether or not the slope was positive or negative to begin with. A higher positive slope means a steeper upward tilt to the line, while a smaller positive slope means a flatter upward tilt to the line. A negative slope that is larger in absolute value (that is, more negative) means a steeper downward tilt to the line. A slope of zero is a horizontal flat line. A vertical line has an infinite slope.<\/p>\n

Suppose a line has a larger intercept. Graphically, that means it would shift out (or up) from the old origin, parallel to the old line. If a line has a smaller intercept, it would shift in (or down), parallel to the old line.<\/p>","rendered":"

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

What the\u00a0Slope Means<\/strong><\/h2>\n

The concept of slope is very useful in economics, because it measures the relationship between two variables. A positive slope<\/strong>\u00a0<\/span>means that two variables are positively related\u2014that is, when x<\/em> increases, so does y<\/em>, and when x<\/em> decreases, y<\/em> decreases also. Graphically, a positive slope means that as a line on the line graph moves from left to right, the line rises. \u00a0We will learn in other sections\u00a0that “price” and “quantity supplied” have a positive relationship; that is, firms will supply more when the price is higher.<\/p>\n

\"A<\/p>\n

Figure 1. Positive Slope<\/strong><\/p>\n<\/div>\n

A negative slope<\/span><\/strong> means that two variables are negatively related; that is, when x<\/em> increases, y<\/em> decreases, and when x<\/em> decreases, y<\/em> increases. Graphically, a negative slope means that as the line on the line graph moves from left to right, the line falls. \u00a0We will learn that “price” and “quantity demanded” have a negative relationship; that is, consumers will purchase less when the price is higher.<\/p>\n

\"A<\/p>\n

Figure 2. Negative slope<\/strong><\/p>\n<\/div>\n

A slope of zero<\/strong> means that there is a constant\u00a0relationship between x<\/em> and y<\/em>. Graphically, the line is flat; the rise over run is zero.<\/p>\n

\"A<\/p>\n

Figure 3. Slope of Zero<\/strong><\/p>\n<\/div>\n

The unemployment-rate graph in Figure 4, below, illustrates a common pattern of many line graphs: some segments where the slope is positive, other segments where the slope is negative, and still other segments where the slope is close to zero.<\/p>\n

\n
\"The<\/p>\n

Figure 4. U.S. Unemployment Rate, 1975\u20132014<\/strong><\/p>\n<\/div>\n<\/figure>\n

Calculating Slope<\/h2>\n

The slope of a straight line between two points can be calculated in numerical terms. To calculate slope, begin by designating one point as the \u201cstarting point\u201d and the other point as the \u201cend point\u201d and then calculating the rise over run between these two points.<\/p>\n

\"The<\/p>\n

Figure 5. Altitude\u2013Air Density Relationship<\/strong><\/p>\n<\/div>\n

As an example, consider the slope of the air-density graph, above, between the points representing an altitude of 4,000 meters and an altitude of 6,000 meters:<\/p>\n

Rise: Change in variable on vertical axis (end point minus original point)<\/p>\n

\n
0.100\u00a0\u2013\u00a00.307\u00a0=\u00a0\u20130.207<\/span><\/span><\/div>\n<\/div>\n

Run: Change in variable on horizontal axis (end point minus original point)<\/p>\n

\n
6,000\u00a0\u2013\u00a04,000=\u00a02,000<\/span><\/span><\/div>\n<\/div>\n

Thus, the slope of a straight line between these two points would be the following: from the altitude of 4,000 meters up to 6,000 meters, the density of the air decreases by approximately 0.1 kilograms\/cubic meter for each of the next 1,000 meters.<\/p>\n

Suppose the slope of a line were to increase. Graphically, that means it would get steeper. Suppose the slope of a line were to decrease. Then it would get flatter. These conditions are true whether or not the slope was positive or negative to begin with. A higher positive slope means a steeper upward tilt to the line, while a smaller positive slope means a flatter upward tilt to the line. A negative slope that is larger in absolute value (that is, more negative) means a steeper downward tilt to the line. A slope of zero is a horizontal flat line. A vertical line has an infinite slope.<\/p>\n

Suppose a line has a larger intercept. Graphically, that means it would shift out (or up) from the old origin, parallel to the old line. If a line has a smaller intercept, it would shift in (or down), parallel to the old line.<\/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>