What makes the slope of a line undefined

In our problem, that would be Looking at the graph, you can see that this graph never crosses the y -axis, therefore there is no y -intercept either. Another way to look at this is the x value has to be 0 when looking for the y -intercept and in this problem x is always 5. So, for all our efforts on this problem, we find that the slope is undefined and the y -intercept does not exist. Looking at the graph, you can see that this graph crosses the y -axis at 0, So the y-intercept is 0, The slope is 0 and the y -intercept is Note that two lines are parallel if there slopes are equal and they have different y -intercepts.

What do you think? The slope of the first equation is 7 and the slope of the second equation is 7. Since the two slopes are equal and their y -intercepts are different, the two lines would have to be parallel. So what does that mean? Since the two slopes are negative reciprocals of each other, the two lines would be perpendicular to each other. The slope of the first equation is and the slope of the second equation is Since the two slopes are not equal and are not negative reciprocals of each other, then the answer would be neither.

At the link you will find the answer as well as any steps that went into finding that answer. 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. However, remember these two unique cases: Horizontal lines have a slope of 0 because the vertical change is 0.

Vertical lines have an undefined slope because the horizontal change is 0 — you cannot divide a number by 0. To use the site, please enable JavaScript in your browser and reload the page.

Enable contrast version. TutorMe Blog. 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. 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.