When is slope 0

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.

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. 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. 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,. 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. All rights reserved. Definition For any two distinct points on a line, x 1 , y 1 and x 2 , y 2 , the slope is,.