When is the slope equals 0

This means the slope is undefined. As shown above, whenever you have a vertical line your slope is undefined. Note how we do not have an x. If you said horizontal, you are correct. Note how all of the y values on this graph are Having 0 in the numerator and a non-zero number in the denominator means only one thing. The slope equals 0. In other words, perpendicular slopes are negative reciprocals of each other. Example 8 : Determine if the lines are parallel, perpendicular, or neither.

In order for these lines to be parallel their slopes would have to be equal and to be perpendicular they would have to be negative reciprocals of each other. Example 9 : Determine if the lines are parallel, perpendicular, or neither. What did you find? Example 10 : Determine if the lines are parallel, perpendicular, or neither. These are practice problems to help bring you to the next level. It will allow you to check and see if you have an understanding of these types of problems.

Math works just like anything else, if you want to get good at it, then you need to practice it. Even the best athletes and musicians had help along the way and lots of practice, practice, practice, to get good at their sport or instrument.

In fact there is no such thing as too much practice. The following are webpages that can assist you in the topics that were covered on this page:.

The slope of a line measures the steepness of the line. Negative slope: Note that when a line has a negative slope it goes down left to right. The slope of the line is The slope of the line is 0.

The slope of the line is undefined. 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. For example, the lines given by the equations,. Let's consider again the two equations we did first on the previous page, and compare the lines' equations with their slope values.

In both cases, the number multiplied on the variable x was also the value of the slope for that line. This relationship will become very important when you start working with straight-line equations. The graph looked like this:. Notice how the line, as we move from left to right along the x -axis, is edging upward toward the top of the drawing; technically, the line is an "increasing" line.

This relationship always holds true: If a line is increasing, then its slope will be positive; and if a line's slope is positive, then its graph will be increasing. Notice how the line, as we move from left to right along the x -axis, is edging downward toward the bottom of the drawing; technically, the line is a "decreasing" line. This relationship is always true: If a line is decreasing, then its slope will be negative; and if a line's slope is negative, then its graph will be decreasing.

This relationship between the sign on the slope and the direction of the line's graph can help you check your calculations: if you calculate a slope as being negative, but you can see from the graph of the equation that the line is actually increasing so the slope must be positive , then you know you need to re-do your calculations. Being aware of this connection can save you points on a test because it will enable you to check your work before you hand it in.

So now we know: Increasing lines have positive slopes, and decreasing lines have negative slopes. With this in mind, let's consider the following horizontal line:.

Is the horizontal line edging upward; that is, is it an increasing line? This means that the line has no slope, and instead appears as a straight line with no positive or negative shift regardless of how far you follow it in either direction.

Zero-slope lines are easy to graph on a two-dimensional plane. Using the standard linear equation of. Similar to the concept of zero-slope lines is the "undefined" or "infinite" line. Just as zero-slope lines have no rise, undefined lines have no run; they don't travel left to right at all. This is actually why they're referred to as "undefined", as trying to enter them into the slope equation results in division by zero since run is the denominator in the slope formula.

Since you can't divide by zero, you're left with a slope that doesn't have a definition.