Graphing Review: Linear Functions and Interpreting Curves, Study notes of Microeconomics

Lecture notes on graphing linear functions, covering the functional form, slope, intercepts, and interpreting curves. It includes examples and explanations of the rise over run method for calculating slope and the concept of constant and changing slope in curves.

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Pre 2010

Uploaded on 03/18/2009

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Graphing Review - Lecture Notes
August 28, 2006
I. Linear functions
A. Functional form
1. y = mx + b
Ex. Consider the budget constraint with the functional form y = -2x + 12
B. Slope
1. Given a unit change in the horizontal axis the slope is the value by which the vertical axis
will change while moving along the curve
2. In the functional form above m is the slope of the line
3. Given two points on a curve one may compute the slope using the "rise over run"
technique
a. Slope = rise/run = (y2 - y1) / (x2 - x1)
Ex. Given points A and E one may compute the slope, rise/run = (6 - 8) / (3 - 2) = -2
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Graphing Review - Lecture Notes

August 28, 2006

I. Linear functions A. Functional form

  1. y = mx + b Ex. Consider the budget constraint with the functional form y = -2x + 12 B. Slope
  2. Given a unit change in the horizontal axis the slope is the value by which the vertical axis will change while moving along the curve
  3. In the functional form above m is the slope of the line
  4. Given two points on a curve one may compute the slope using the "rise over run" technique a. Slope = rise/run = (y2 - y1) / (x2 - x1) Ex. Given points A and E one may compute the slope, rise/run = (6 - 8) / (3 - 2) = -
  1. Extreme cases a. The slope of a vertical line is infinite b. The slope of a horizontal line is zero C. Intercepts
  2. Vertical or y intercept a. When x is equal to zero at what value does the line cross the vertical axis b. In the functional form above it may be seen that if x = 0, then y = b, therefore b is the y-intercept Ex. In the example the y-intercept is b = 12
  3. Horizontal or x intercept a. When y is equal to zero at what value does the line cross the horizontal axis b. In the functional form above it may be seen that if y = 0, then x = -b/m, therefore -b/m is the x-intercept Ex. In the example the x-intercept is -b/m = -12 / -2 = 6
  1. Notice that the slope has changed from point E to point A C. Beware of a graph's scale Ex. The curves presented below are identical