What kind of line has a slope of zero

Linear functions are graphically represented by lines and symbolically written in slope-intercept form as,. The Definition of Slope :. Slope is defined as the ratio of the rise of the line i. For any two distinct points on a line, x 1 , y 1 and x 2 , y 2 , the slope is,. Intuitively, we can think of the slope as measuring the steepness of a line. The slope of a line can be positive, negative, zero, or undefined.

A horizontal line has slope zero since it does not rise vertically i. As stated above, horizontal lines have slope equal to zero. This does not mean that horizontal lines have no slope. Functions represented by horizontal lines are often called constant functions.

It doesn't matter which one you call point 1 and which one you call point 2 as long as you are consistent throughout that problem. Make sure that you are careful when one of your values is negative and you have to subtract it as we did in line 2.

Example 2 : Find the slope of the straight line that passes through 1, 1 and 5, 1. It is ok to have a 0 in the numerator. Remember that 0 divided by any non-zero number is 0. Example 3 : Find the slope of the straight line that passes through 3, 4 and 3, 6. Since we did not have a change in the x values, the denominator of our slope became 0.

This means that we have an undefined slope. If you were to graph the line, it would be a vertical line, as shown above. If your linear equation is written in this form, m represents the slope and b represents the y -intercept. Example 4 : Find the slope and the y -intercept of the line. Lining up the form with the equation we got, can you see what the slope and y-intercept are?

Example 5 : Find the slope and the y -intercept of the line. This example is written in function notation, but is still linear. As shown above, you can still read off the slope and intercept from this way of writing it. Note how we do not have a y. This type of linear equation was shown in Tutorial Graphing Linear Equations. If you said vertical, you are correct. Note that all the x values on this graph are 5.

Well you know that having a 0 in the denominator is a big no, no. 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? Well, again, kind of. So maybe the slope will be negative? The concept of slope simply does not work for vertical lines.

The slope of a vertical line does not exist! Let's do the calculations to confirm the logic. From the line's graph, I'll use the arbitrary points 4, 5 and 4, —3. Then the slope is:. We can't divide by zero, which is of course why this slope value is "undefined".

This relationship is always true: a vertical line will have no slope, and "the slope is undefined" or "the line has no slope" means that the line is vertical. Any time your line involves an undefined slope, the line is vertical; and any time the line is vertical, you'll end up dividing by zero if you try to compute the slope.

Warning: It is very common to confuse these two types of lines and their slopes, but they are very different. Just as "horizontal" is not at all the same as "vertical", so also "zero slope" is not at all the same as "no slope". Just as a "Z" with its two horizontal lines is not the same as an "N" with its two vertical lines , so also "Zero" slope for a horizontal line is not the same as "No" slope for a vertical line.

The number "zero" exists, so horizontal lines do indeed have a slope. But vertical lines don't have any slope; "slope" simply doesn't have any meaning for vertical lines. It is very common for tests to contain questions regarding horizontals and verticals. Don't mix them up!