The slope of a line measures the steepness of the line or the slant of the line. You can
calculate slope by finding the change in Y and dividing it by the change in x. Sometimes
this is referred to as the "rise over run".
Rise means how many units you move up or down from point to point. On the graph
that would be a change in the y values.
Run means how far left or right you move from point to point. On the graph, that would
mean a change of x values.
Here are some examples of slope.
Positive slope: A line has a positive slope if it goes up from left to right.
Negative slope: A line has a negative slope if it goes down from left to right.
Zero slope: A line has a zero slope if it is horizontal.
Undefined Slope: A line has an undefined slope if it is vertical.
How do we calculate 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.
Remember slope is defined as the change in the y-coordinates divided by the
change in the x-coordinates, or the rise over the run. Writing "change in x-
coordinates" and "change in y-coordinates" 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 (x1, y1) and our second point (x2, y2), we can rewrite our
formula to get rid of the delta:
We can use this formula to find the slope of our example line.
Change in Y:
Change in X:
Divide Y by X:
How can we describe in words what is happening to the slope of our line?
How is the concept of slope used in everyday life?