Calculating Slope and Using Slope Intercept Form
This week we began a new unit which was all about the slope of graph, in other words how a steep a line is. When calculating the slope we will need to find a specific number that describes the steepness of the line. Calculating the slope is not very complicated, however it is one of the most important skills in graphing if not the most important. It opens the door to taking further steps and finding more about the graph. In this blog post we are going to look at how to calculate the slope and furthermore, put this to use in writing an equation in slope intercept form.
Here is the first example we are going to be working with:
Step 1 – rise/run: the equation to calculate the slope of a line is the change in y over the change in x or in the other words “rise over run”.
Step 2 – calculating the slope: to calculate the slope of a line it is actually quite simple, you just need to make sure you look at the change in the y (rise) first. If you look at the change in the x (run) first, the slope will turn out to be very different. So first we are going to choose any point on the line and look how far up the next point is. In this case the next point is four spaces up, we now have our rise. Next we look how far the point is moved horizontally (in this case to the right which means it is a positive change) and it is only one spot to the right, we now have our run. So the slope here would be 4/1 but that can be changed to just 4.
Step 3 – writing the equation in slope intercept form: in order to write an equation in slope intercept form you simply need to write y equals the slope times x plus another number. The formula for this equation is y=mx+b. To find b it is quite straightforward, all you need to do is find the y-intercept on the graph. Once you have found this you can insert it into the equation. The equation should look like this:
Example 2:
We are now going to look at a graph with a line that has a slope that looks a little different.
Here is the graph and line we are going to be working with:
Step 1 – rise/run: the equation to calculate the slope of a line is the change in y over the change in x or in the other words “rise over run”.
Step 2 – calculating the slope: to calculate the slope of a line it is actually quite simple, you just need to make sure you look at the change in the y (rise) first. If you look at the change in the x (run) first, the slope will turn out to be very different. So first we are going to choose any point on the line and look how far up the next point is. In this case the next point is one space up, we now have our rise. Next we look how far the point is moved horizontally (in this case to the right which means it is a positive change) and it is two spots to the right, we now have our run. So the slope here would be 1/2. Yes, this is a fraction, however this makes no difference, it doesn’t make anything more difficult even though it may seem like it might.
Step 3 – writing the equation in slope intercept form: in order to write an equation in slope intercept form you simply need to write y equals the slope times x plus another number. The formula for this equation is y=mx+b. To find b it is quite straightforward, all you need to do is find the y-intercept on the graph. Once you have found this you can insert it into the equation. Again, this line has a fraction as its slope, this does not change anything. The equation should look like this:
Summary:
That is how you find the slope and write an equation for a line in slope intercept form. I believe that this skill is the most important part of graphing since you can do so many things once you have found the slope of a line. Without this skill graphing can become very difficult. This is a fairly simple thing to learn and once you get it, calculating the slope will become second nature.