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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