Lines and Slope  Chameleon Home  Ask Dr. Math 

Calculating Slope We can tell whether a line's slope is big or small, and whether the slope is positive or negative. But what if we want to compare two big slopes, or two small slopes? We need a more exact definition of slope. Let's start by drawing a line and picking two points on the line. (There's nothing special about this line or these points  we just want an example.) Slope is defined as the change in the ycoordinates divided by the change in the xcoordinates. People often remember this definition as "rise/run." In this picture, the change in ycoordinates (rise) is red, and the change in xcoordinates (run) is blue: Writing "change in xcoordinates" and "change in ycoordinates" many times is a lot of work, so let's use the Greek letter delta, , as an abbreviation for change. The traditional abbreviation for slope is m. Now we can write a formula for slope: If we name our first point (x_{1}, y_{1}) and our second point (x_{2}, y_{2}), we can rewrite our formula to get rid of the delta: We can use this formula to find the slope of our example line. Our first point was
= (4  2) / (2  1) = 2/1 = 2. Now we know that the slope of our line is 2. You can see from the graph that the line moves up two spaces for every space that it moves to the right: 
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