Video: Calculating the Slope of a Line

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Calculating the Slope of a Line

 
 
The Questions
In Physics class, data is often collected and plotted in order to determine a relationship between the two quantities under study. The analysis often involves a slope calculation. What is meant by slope? And how is the slope calculated? I'm Mr. H and I have some answers for you.
 
 
What is Slope?
Slope refers to how steep a line is. It is the ratio of the Rise per Run. The Rise refers to the change in Y-coordinate value between any two points on the line; this is called ∆Y. The Run refers to the change in X-coordinate for those same two points; this is ∆X. The slope is calculated as the ∆Y divided by the ∆X. 
 
 
How is Slope Calculated?
Let me demonstrate a simple 5-step process for calculating the slope. 
First, identify the coordinates of two points that are on the line. Select points that are on the line and whose coordinates are clearly known. So I'm going to select these two points. They're on the line. And I can clearly determine their coordinates without a lot of estimating.
 
Second, write the coordinates down in (X, Y) format. X refers to the horizontal axis value and Y refers to the vertical axis value. This point has (X₁, Y₁) coordinates of (0.0 s, 4.0 m). And this point has (X₂, Y₂) coordinates of (6.0 s, 22.0 m). 
 
Third, calculate the Rise or the change in the Y-coordinate value. That's Y₂- Y₁or 22.0 m - 4.0 m. ∆Y = 18.0 m
 
Fourth, calculate the Run or the change in the X-coordinate value. That's X₂- X₁or 6.0 s - 0.0 s. ∆X = 6.0 s
 
Now calculate the slope by dividing the ∆Y by the ∆X. Show your work. Show your answer. Show your unit. Show you're great! 18.0 m / 6.0 s = 3.0 m/s. The units will always be the Y-coordinate unit divided by the X-coordinate unit.
 
Warning #1
I have two warnings for you ... two things you should be aware of. The first has to do with lines that pass through the origin. When you're calculating slope for a graph like this, select the origin point as one of your points. That is, choose (X₁, Y₁) to be (0.0 s, 0.0 m). This choice simplifies the math. Because now the Rise or ∆Y will be the Y₂value. And the Run or ∆X will be the X₂value. So the slope or Rise per Run will be Y₂/X₂.
 
But do be careful! Just because the slope is Y₂/X₂under these conditions doesn't mean it is always Y₂/X₂. The slope is always the ∆Y/∆X ratio.
 
 
Warning #2
Now the second warning has to do with downward sloping lines ... like this. When you do your math [ .. PAUSE .. ], your slope value comes out to be negative. Downward-sloping lines will always have negative slope values. So if your calculations yield a positive value, go back and check your wok. Oh ... you did show your work, didn't you?
 
 
Conclusion
In the Description section of this video, you will find links to some awesome interactive exercises on our website. Putting this lesson and the 5-step process to practice is a great way to ensure that You Got This!
 
I'm Mr. H. Thanks for watching!
 

 

 

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