Why slope of vertical line undefined

Slope is defined as the steepness, incline, or gradient of a line. It is also defined as the change in y value "rise" over the change in x value "run". The slope formula is:. Here, the variable m represents the slope. You can have a positive slope or negative slope depending on its value. That means it has no slope! We'll show you why this is a little later. This means for each unit increase in x , there is a corresponding m unit increase in y i.

Lines with positive slope rise to the right on a graph as shown in the following picture,. Lines with greater slopes rise more steeply.

This means for each unit increase in x , there is a corresponding m unit decrease in y i. Lines with negative slope fall to the right on a graph as shown in the following picture,.

The steepness of lines with negative slope can also be compared. Specifically, if two lines have negative slope, the line whose slope has greatest magnitude known as the absolute value falls more steeply. Two lines in the xy -plane may be classified as parallel or perpendicular based on their slope.

Parallel and perpendicular lines have very special geometric arrangements; most pairs of lines are neither parallel nor perpendicular. Parallel lines have the same slope. On the line below, no matter what the value of y, x is always equal to 1. Since x never changes, the run will always be 0. This is true for any vertical line Vertical lines do not have positive slopes or negative slopes.

They have undefined slopes. Now, let's write this out with variables. We can use points x1,y1 and x2,y2 to figure out the slope. The y-values dictate the vertical position, or rise. The x-values dictate horizontal position, or run. The x value of any two points doesn't change for any vertical line. This gives us a fraction with a 0 in the denominator. We cannot divide by zero , so our slope is undefined. The picture above shows how every vertical line, no matter where it is on the x-axis, has an undefined slope.

This is because the denominator of the rise over run fraction is always 0.