1. © Pearson Education Canada, 2003 GRAPHS IN ECONOMICS 1 APPENDIX

2. © Pearson Education Canada, 2003 Graphs Used in Economic Models Graphs are used in economic models to show the relationship between variables. The patterns to look for in graphs are the four cases in which:  Variables move in the same direction  Variables move in opposite directions  Variables have a maximum or a minimum  Variables are unrelated

3. © Pearson Education Canada, 2003 Graphs Used in Economic Models Variables That Move in the Same Direction A relationship between two variables that move in the same direction is called a positive relationship or a direct relationship. A line that slopes upward shows a positive relationship. A relationship shown by a straight line is called a linear relationship. The three graphs on the next slide show positive relationships.

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5. Graphs Used in Economic Models Variables That Move in Opposite Directions A relationship between two variables that move in opposite directions is called a negative relationship or an inverse relationship. A line that slopes downward shows a negative relationship. The three graphs on the next slide show negative relationships.

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7. Graphs Used in Economic Models Variables That Have a Maximum or a Minimum The two graphs on the next slide show relationships that have a maximum and a minimum. These relationships are positive over part of their range and negative over the other part.

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9. Graphs Used in Economic Models Variables That are Unrelated Sometimes, we want to emphasize that two variables are unrelated. The two graphs on the next slide show examples of variables that are unrelated.

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11. The Slope of a Relationship The slope of a relationship is the change in the value of the variable measured on the y-axis divided by the change in the value of the variable measured on the x-axis. We use the Greek letter  (capital delta) to represent “change in.” So  y means the change in the value of the variable measured on the y-axis and  x means the change in the value of the variable measured on the x-axis. The slope of the relationship is  y/  x.

12. © Pearson Education Canada, 2003 The Slope of a Relationship The Slope of a Straight Line The slope of a straight line is constant. Graphically, the slope is calculated as the “rise” over the “run.” The slope is positive if the line is upward sloping.

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14. The Slope of a Relationship The slope is negative if the line is downward sloping.

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16. The Slope of a Relationship The Slope of a Curved Line The slope of a curved line at a point varies depending on where along the curve it is calculated. We can calculate the slope of a curved line either at a point or across an arc.

17. © Pearson Education Canada, 2003 The Slope of a Relationship Slope at a Point The slope of a curved line at a point is equal to the slope of a straight line that is the tangent to that point. Here, we calculate the slope of the curve at point A.

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19. The Slope of a Relationship Slope Across an Arc The average slope of a curved line across an arc is equal to the slope of a straight line that joins the endpoints of the arc. Here, we calculate the average slope of the curve along the arc BC.

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21. Mathematical Note Figure 1 shows a linear relationship—a relationship between two variables that graphs as a straight line. A linear equation describes a linear relationship between x and y as y = a + bx

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23. Mathematical Note The slope of a relationship is the change in y,  y, divided by the change in x,  x or  y/  x In Figure 2, y 1 = a + bx 1 and y 1 +  y = a + b(x 1 +  x)

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25. Mathematical Note To calculate the slope of the line, subtract the first equation y 1 = a + bx 1 from the second equation y 1 +  y = a + b(x 1 +  x) to obtain  y = b  x

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27. Mathematical Note Now divide both sides by  x to obtain  y/  x = b The slope of the line is b.

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29. Mathematical Note If a changes, the relationship shifts, as you can see in Figure 3.

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31. Mathematical Note If b is positive, the relationship is described by an upward-sloping line like those in Figures 1, 2, and 3. If b is negative, the relationship is described by a downward-sloping line like that in Figure 4.

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33. GRAPHS IN ECONOMICS 1 APPENDIX THE END