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. 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,. 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,. 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. To understand the discussion below, you should be familiar with finding the slope using the slope formula.
Now, we can see the issue. Since the two x-values were the same, the denominator of the slope ends up being 0.
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