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Slope

Slope: the slant of a line -- the ratio of the change in the y-axis to the change in the x-axis between two points on a line

PROPERTY OF STRAIGHT LINES: SLOPE REMAINS CONSTANT

**Any two points will have the same slope.**

Some people like to think of slope as:

  rise
  
  run

Others think of it as:

  y2 - y1

 
x2 - x1

in which y2 and y1 are the two y coordinates and x2 and x1 are the two x coordinates.  Remember: y2 and x2 must be from the same point, as x1 and y1 must be (there is point 1 and point 2).

Example:

Let us take the equation we had...x + y = 4

The graph was:

Let's pick 2 points from this line...(1,3) and (4,0)

x1 = 1, x2 = 4
y1 = 3, y2 = 0

x2 - x1                   4 - 1                        3
      =          =            =  -1
y2 - y1                   0 - 3                   -3

** "m" denotes slope....so in this equation, m = -1

**Often slope IS A FRACTION...this turned out to be an integer.**

AS A RULE OF THUMB: Any line going up on the left will have a negative slope...any line going up on the right will have a positive slope.

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