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Understanding Graphs

Understanding Graphs. CHAPTER 1 Appendix. Graph. Picture showing how variables relate and conveys information in a compact and efficient way Functional relation exists between two variables when the value of one variable depends on another

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Understanding Graphs

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  1. Understanding Graphs CHAPTER 1 Appendix

  2. Graph • Picture showing how variables relate and conveys information in a compact and efficient way • Functional relation exists between two variables when the value of one variable depends on another • The value of the dependent variable depends on the value of the independent variable

  3. Exhibit 4: Basics of a Graph • The value of variable x is measured along the horizontal axis and increases as you move to the right of the origin. • The value of the variable y is measured along the vertical axis and increases as you move upward. • Any point on a graph represents a combination of particular values of two variables. • For example, point a represents the combination of 5 units of variable x and 15 units of variable y, while point b represents 10 units of x and 5 units of y.

  4. Exhibits 6 & 7:Relating Distance Traveled to Hours Driven Hours Distance Driven Traveled Per Per Day Day (miles) a 1 50 b 2 100 c 3 150 d 4 200 e 5 250

  5. Slopes of Straight Lines • Indicates how much the vertical variable changes for a given change in the horizontal variable • Vertical Change divided by the horizontal Change • Slope = Change in the vertical distance / change in the horizontal distance

  6. Exhibit 8: Alternative Slopes for Straight Lines 8a.) Positive relation

  7. Exhibit 8: Alternative Slopes for Straight Lines 8b.) Negative relation

  8. Exhibit 8: Alternative Slopes for Straight Lines 8c.) No relation: zero slope

  9. Exhibit 8: Alternative Slopes for Straight Lines 8d.) No relation: infinite slope

  10. Exhibit 9: Slope Depends on the Unit of Measure Total Cost a) Slope = 1/1 = 1 b) Slope = 3/1 = 3 Total Cost $6 $6 1 5 3 1 3 1 0 0 5 6 1 2 Feet of copper tubing Yards of copper tubing

  11. Slope and Marginal Analysis • Economic analysis usually involves marginal analysis • The slope is a convenient device for measuring marginal effects because it reflects the change in one variable – the effect -- compared to the change in some other variable – the cause • Slope of straight line is the same everywhere along the line

  12. A a B b B A Exhibit 10: Slopes at Different Points on a Curved Line y Slope of curved line varies at different points along curve 40 Draw a straight line that just touches the curve at a point but does not cut or cross the curve – tangent to the curve at that point With line AA tangent to the curve at point a, the horizontal value increases from 0 to 10 while the vertical value falls from 40 to 0  slope of -4 30 20 Slope of the tangent at that point is the slope of the curve at that point 10 0 10 20 30 40 x

  13. a b Exhibit 11: Curves with Both Positive and Negative Ranges y The U-shaped curve begins with a negative slope, has a slope of 0 at point b, and a positive slope after point b. The hill-shaped curve begins with a positive slope to the left of point a, a slope of 0 at point a, and a negative slope to the right of point a. x

  14. Exhibit 12: Shift in Curve Relating Distance Traveled to Hours Driven T' f ) s e l i T m ( 250 y a d d r 200 e p d A change in the assumption about average speed changes the relationship between the two variables. 150 e l e v a 100 r t e c n 50 a t s i D 0 1 2 3 4 5 Hours driven per day

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