Working%20With%20Graphs

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Working With Graphs
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Graphs In General

• A graph is a visual representation of the
  relationship between two or more variables.
• We will deal with just two variables at a time.

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Graphs In General

• 1. Independent variable This is the variable
  that influences the dependent variable. (X
  variable)
• 2. Dependent variable Its value is determined
  by the independent variable. (Y variable)

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Graphs In General

• 3. We say that the dependent variable is a
• function of the independent variable
• Y f(X)

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The Axis of a Graph

• Dependent Variable
• (Y-axis)
• Independent Variable (X-axis)

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Direct Relationships

• A person's weight and height are often related.
• If we sample 1000 people and measure their weight
  and height we would probably find that as weight
  increases so does height.

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Direct Relationships

• Height
• Weight

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Direct Relationships

• There is a direct relationship between height and
  weight.
• Have a direct relationship when
• ? indep. variable ? dep. variable ?
• ??indep. variable ? dep. variable ?

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Inverse Relationships

• There is strong evidence indicating that as price
  rises for a specific commodity, the amount
  purchased decreases.

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Inverse Relationships

• Price per Unit
• Demand
• Curve
• Quantity Purchase per Unit Time

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Inverse Relationships

• There is an inverse relationship between price
  per unit and the quantity purchased per unit of
  time.
• Have an inverse relationship when
• (1) indep. variable ? ? ? dep. variable
• (2) indep. variable ????????dep. variable

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Complex Relationships

• Evidence suggests that income from wages
  increases up to a certain age, and then decreases
  until death.

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Complex Relationships

• Income from Wages ()
• Age

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Complex Relationships

• There is a direct relationship between wage
  income and age up to a certain point known as
  retirement,
• then an inverse relationship exists from
  retirement to the individuals expiration date.

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Complex Relationships

• Income from All Sources ()
• Age

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Complex Relationships

• Income from All Sources ()
• Age

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Complex Relationships

• Income from All Sources ()
• Age

What should the slope of this line be equal to at
the minimum?
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Constructing A Graph

• We start with a horizontal number line

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Constructing A Graph

• 1. The points on the line divide the line into
  segments.
• 2. All the line segments are equally spaced
• 3. Numbers associated with the points increase in
  value from left to right.
• 4. Use a distance, so many points, to represent a
  quantity.

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Constructing A Graph
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Add a Vertical Number Line

• 1. Construct a vertical number line.
• 2. Points divide the line into equal
• segments.
• 3. Numbers associated with points
• increase in value from the
  bottom
• to top.
• 4. The scale can be different from the
• horizontal number line.

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Add a Vertical Number Line
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To Make A Graph

• 1. The vertical and horizontal number lines must
  intersect at each others zero point.
• 2. They must be perpendicular.

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To Make A Graph

• The vertical and horizontal number lines should
  look like the illustration below

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To Make A Graph

• 3. Result We get a set of coordinate axis, or
  a coordinate number system.
• e.g. Sighting in a rifle scope on the range.

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How would you call out the location of this three
shot group?
X-Axis
Y-Axis
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To Make A Graph

• 4. With a graph, you need two numbers to specify
  a single point
• OR
• When you see a point on a graph, you know that
  point represents two numbers !

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BASICS YOU NEED TO KNOW ABOUT GRAPHING AND THE
COORDINATE NUMBER SYSTEM

• Axis defined
• The vertical number line is reserved for the
  Dependent variable and is referred to as the Y
  AXIS.
• The horizontal number line is referred to as the
  X AXIS and is reserved for the Independent
  variable.

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The origin and points on the graph

• The point of intersection of the two number lines
  is referred to as the ORIGIN.

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• Point A represents two numbers A value for x
  and a value for y.

32??0
Point A
???????
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The origin and points on the graph

• Every point on a graph represents a pair of
  observations of x and y.
• (x,y)
• In this class, y will often represent price and x
  will often represent quantity.

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The Slope

• 1. Slope change in Y values / change in X
  values
• (y1 - y0) / (x1 - x0)
• RISE / RUN

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The Slope

• Price
• 8
• 6
• 2 3 Quantity demanded per unit time

???????????x0, y0)
????????x1, y1)
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The Slope

• 2. As X goes from 2 to 3,
• Y goes from 8 to 6.
• 3. ? Y RISE (TO - FROM) 6 - 8 -2
• ? X RUN (TO - FROM) 3 - 2 1

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The Slope

• 4. SLOPE ?Y / ?X -2 / 1 -2
• 5. The slope of a straight line is CONSTANT.
• Class Exercise

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References

• N.c.State university-College of Agriculture and
  Life science Dr. herman_sampson