What type of line has an undefined slope

To understand the discussion below, you should be familiar with finding the slope using the slope formula. Now, we can see the issue. Since the two x-values were the same, the denominator of the slope ends up being 0.

Division by zero is always undefined. Every point on this line has an x-coordinate of 4, so this will happen regardless of the points picked. 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. For example, the lines given by the equations,. These two lines have different y -intercepts and will therefore never intersect one another since they are changing at the same rate both lines fall 3 units for each unit increase in x. The graphs of y 1 and y 2 are provided below,. Perpendicular lines have slopes that are negative reciprocals of one another. In other words, if a line has slope m 1 , a line that is perpendicular to it will have slope,.

The graphs of y 3 and y 4 are provided below,. Vertical lines have undefined slopes. This is because no matter how much their height position on the y-axis changes, their position on the x-axis never does. This means that even if their rise is infinite, their run will always be 0. Here are some examples with random values for rise:. It's impossible to divide by 0.

A fraction with 0 as its denominator will always be undefined. 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.