Definition: The slope is the rate of change of a line, that is the: "vertical change"/"horizontal change".

Introduction to Slopes - See, Hear & Do - Money in the Bank  NEW!

To calculate the slope we "pick" points on the line A(1,-4) and B(4,2).
We will look "from A to B".
The "change in x" "from A to B" is 4-1=3.
The "change in y" "from A to B" is 2-(-4)=2+4=6.
Slope of this line = m =  \frac{\mbox{vertical change}}{\mbox{horizontal change}} = \frac{6}{3} = 2

The equation of this line is: y=2x-6   or   2x-y=6 .

What if we "pick" different points?

This is the same line as above.

Let's "pick" the points root=(3,0) and y-intercept=(0,-6).

     Remember - we subtract "second point" - "first point".
"change in x" = 0-3 = -3 and "change in y" = -6-0 = -6
Slope = m =  \frac{\mbox{vertical change}}{\mbox{horizontal change}} = \frac{-6}{-3} = 2 .
Slope is same no matter what points we "pick".

BUT you must do the subtractions in the same direction!

Which comes first: x or y?

  • Coordinates of a point are (x,y) so when graphing a point do horizontal then vertical. See&Do
  • Slopes are   \frac{\mbox{vertical change}}{\mbox{horizontal change}}   - so with slope the vertical change is above the horizontal change in the fraction!
  • Think: slope=speed. Speed is measured distance/time (mph or m/s) where time = x-axis and distance = y-axis.

Calculating the slope of a line:

  1. Pick any 2 points on the line.
  2. Arbitrarily decide which is the "first point" and "second point".
  3. "change in x" = "x-coordinate of second point" - "x-coordinate of first point".
  4. "change in y" = "y-coordinate of second point" - "y-coordinate of first point".
  5. slope =   \frac{\mbox{change in y}}{\mbox{change in x}}

Rule: The slope of a line is a number. Parallel lines have the same slope.

InterActivities: 5 InterActivities to Practice Slope

Related Topics


Global Slope of a line
Brief Mathcasts and Interactivities to understand and practice the slope of a line in the Cartesaian plane.
Grade 7-10    Interactivities start at 7th grade level on up
Strand Algebra and Functions / Geometry and Measurement
Standard CA 7AF.3.3, Algebra 1 2.5, ACT GR 20-23, ACT GR 24-27   
Keywords line, slope, linear equation, change in y, change in x, ratio
Comments none
Author LFS - contact - website
Type Freeware - Available for School and Offline and Online Use - Translatable (html)
Use Requires sunJava player
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Page last modified on February 04, 2009, at 03:44 AM