But considering this, how can we have an undefined slope? The answer is based on how we calculate slope with the slope formula. In this lesson, we will look at what kinds of lines have an undefined slope and at why this is the case. Any vertical line, like the one shown below, will have an undefined 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,. In the next section we will describe how to solve linear equations. In our problem, that would have to be In this form, the y -intercept is b , which is the constant.
In our problem, that would be 2. We can get down to business and answer our question of what are the slope and y -intercept. In our problem, that would have to be 2. 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.
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. Put simply, a zero slope is perfectly flat in the horizontal direction. The equation of a line with zero slope will not have an x in it. Remove the parentheses around the expression 0,6 0 , 6. The equation is not linear, so the slope does not exist. The equation for a zero slope line is one where the X value may vary but the Y value will always be constant.
Slope, sometimes referred to as gradient in mathematics, is a number that measures the steepness and direction of a line, or a section of a line connecting two points, and is usually denoted by m. A zero slope is just the slope of a horizontal line!
The y-coordinate never changes no matter what the x-coordinate is! In this tutorial, learn about the meaning of zero slope. Thus that line is horizontal slope of 0. Thus that line is vertical undefined slope.
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