How to See if a Graph Is Proportional

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You can see if a graph is proportional by considering the many points that compose the line. See if a graph is proportional with help from an experienced mathematics professional in this free video clip.

Part of the Video Series: Trigonometry, Graphs, & Other Math Tips
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Video Transcript

Hi, my name is Walter Unglaub, and this is how to see if a graph is proportional. So in this example I consider a graph here in which I have a line that is composed of many different points. And I considered just the integer points. And I can examine them so the different coordinates would be one comma two for point A. And then for point B I have two comma three. And then for point C I have three comma four. And what we really mean by proportional is that the relationship between the X values and the Y values are linear. So if the relationship is linear then we can write down the slope intercept equation Y is equal to MX plus B. And we can use our data from our graph to test whether indeed we have proportionality here. We see that the Y intercept is equal to one. So B is going to be equal to one. And we can calculate the slope between any of these two points. So if we consider for example the set of points A and B we have M is equal to the difference in the Y values, three minus two. Divided the difference in the X values, two minus one. So we have one over one which is simply equal to one. And we can test the other set of points B and C for example. So this is M, A, B and M, B, C is equal to four minus three, divided by three minus two. Which again is also equal to one. So we see that indeed there is linear behavior in this graph from the data that we've collected. And so we can write our slope intercept equation as Y is equal to one times X, plus one. So the constant of proportionality then would be the slope which is just M. And that's equal to one. So indeed we see for this example that our graph is indeed proportional. My name is Walter Unglaub and this is how to see if a graph is proportional.

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