What happens if there is no slope

Practice Problem 1a - 1b: Find the slope of the straight line that passes through the given points. Practice Problems 2a - 2c: Find the slope and the y -intercept of the line. Practice Problems 3a - 3b: Determine if the lines are parallel, perpendicular, or neither. Practice Problem 4a: Determine the slope of the line. Need Extra Help on these Topics?

After completing this tutorial, you should be able to: Find the slope given a graph, two points or an equation. This tutorial takes us a little deeper into linear equations. Rise means how many units you move up or down from point to point. On the graph that would be a change in the y values. The subscripts just indicate that these are two different points.

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. The slope of a line is defined as its rise the amount that it travels up or down on a graph as it moves from point to point divided by its run the amount that it travels left to right between those same two points. If the slope of the line doesn't travel up or down, however, the slope ends up being zero divided by the run of the line.

As zero divided by any number is still zero, the overall slope of the line ends up being zero itself. 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. 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. Vertical lines have undefined slope. Since any two points on a vertical line have the same x -coordinate, slope cannot be computed as a finite number according to the formula,. 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,.