Working With Graphs. 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. Graphs In General:.
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A graph is a visual representation of the relationship between two or more variables.
We will deal with just two variables at a time.
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)
3. We say that the dependent variable is a
function of the independent variable:
Y = f(X)
Independent Variable (X-axis)
indep. variable dep. variable
indep. variable dep. variable
There is strong evidence indicating that as price rises for a specific commodity, the amount purchased decreases.
Price per Unit
Quantity Purchase per Unit Time
(1) indep. variable dep. variable
(2) indep. variable dep. variable
Income from Wages ($)
Income from All Sources ($)
What should the slope of this line be equal to at the minimum?
Social Security was NEVER intended to provide benefits sufficient to be the sole source of retirement income.
Current “Social Security” tax rate:
OASDI TAX: Old Age, Survivors, and Disability Insurance.
The 2000 rate of tax is 6.2 percent to a taxable wage limit of $76,200.
The maximum tax an employee may pay is $4,501.20
HI TAX: Federal Hospital Insurance.
The 2000 rate of tax is 1.45 percent without a wage limit.
The maximum tax is therefore unlimited
"Baby Boomers" start
2010 3.5 hitting 65 in 2010
> 2020 2.1
We start with a horizontal number line:
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.
1. Construct a vertical number line.
2. Points divide the line into equal
3. Numbers associated with points
increase in value from the bottom
4. The scale can be different from the
horizontal number line.
1. The vertical and horizontal number lines must intersect at each others zero point.
2. They must be perpendicular.
The vertical and horizontal number lines should look like the illustration below:
3. Result: We get a set of coordinate axis, or a coordinate number system.
e.g. Sighting in a rifle scope on the range.
out the location
of this three shot group?
4. With a graph, you need two numbers to specify a single point
When you see a point on a graph, you know that point represents two numbers !
1. Slope = change in Y values / change in X values
= (y1 - y0) / (x1 - x0)
= RISE / RUN
2 3 Quantity demanded per unit time
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
4. SLOPE = Y / X = -2 / 1 = -2
5. The slope of a straight line is CONSTANT.