Slope as a Ratio


Slope is a measure of how steep a line is.  It can be written as a ratio:  how much the line is rising compared (divided by) to how much it’s moving forward.  This can be expressed as rise over run.  If a line is pointed up and to the right, it has a positive slope.  If it is pointed up and to the left, it has a negative slope.  A vertical line has an undefined slope and a horizontal line has no slope.




Slope Formula


Since a line rising is change in its position on the y-axis, and how much it’s moving to the side is its change in its position on the x-axis, it can be expressed as change in y over  (divided by) change in x.  This is shown in the slope formula, which can be used to calculate the slope between two points without using a graph: 



Plug the x and y coordinates from you two points into the formula and solve for m.  ‘m’ is the variable that typically represents slope in formulas.