The Slope of a Line

Rise over Run

The Angle From the Horizontal - Rise Over Run

When the slope of the line is 0, you know that the line is horizontal and you know it's a vertical line when the slope of a line is undefined.

n the Image, the subscripts on point A, B and C indicate the fact that there are three points on the line. The change in y whether up or down is divided by the change in x going to the right, this is the 'rise over run' concept

y = mx + b is the equation that represents the line and the slope of the line with respect to the x-axis which is given by tan q = m. This is the slope-intercept form of the equation of a line. (m for slope? Seems to be the standard!)

When the slope passes through a point A(x1, y1) then y1 = mx1 + b or with subtraction y - y1 = m (x - x1)

You now have the slope-point form of the equation of a line.

You can also express the slope of a line with the coordinates of points on the line. For instance, in the above figure, A(x, y) and B(s, y) are on the line y= mx + b :

m = tan q =  therefore, you can use the following for the equation of the line AB:

The equations of lines with slope 2 through the points would be:

For (-2,1) the equation would be: 2x - y + 5 = 0.

For (-1, -1) the equation would be: 2x - y + 1 = 0

The slope of a line can real life uses such as building stairs and ramps.  The slope of a incline or decline is important in the construction of roads and important to ski racers and mountaineers.

See slope of a line.