In mathematics, "slope" is the term used to describe a line gradient. It's a measure of the degree to which a line rises and falls. An infinite slope is one of four types of slopes.

All slopes of lines graphed on a Cartesian coordinate plane can be classified as positive, negative, zero or infinite. Lines with positive slopes can be thought of as running "uphill," while lines with negative slopes run "downhill." Lines whose slope is zero are horizontal.

An infinite slope is simply a vertical line. When you plot it on a line graph, an infinite slope is any line which runs parallel to the y-axis. You can also describe this as any line that doesn't move along the x-axis but stays fixed at one constant x-axis coordinate, making the change along the x-axis 0.

The formula for determining the slope of a line is the change in Y divided by the change in X equals slope (m).

Suppose that a single line crosses these two points on a line graph: (2,5) and (2,10). To figure the change in Y for this line, subtract the Y coordinates -- 5 from 10 -- which equals 5. To figure the change in X for this line, subtract the X coordinates -- 2 from 2 -- which equals 0. Now you’re set to apply the slope formula, which, in this example, is 5 divided by 0.

There's no resolution for a number divided by 0 because you can't divide any number by 0. As a result, slopes with no measured change along the x-axis are called infinite.