How to See if a Graph Is Linear

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Seeing if a graph is linear means seeing if it forms a straight line. See if a graph is linear 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

Hello, my name is Walter Unglaub. And this is how to see if a graph is linear. So, here I have a graph and I've labeled three different points, points A, B and C along the line. And I want to see if this is indeed a linear graph. To do that, I would actually have to calculate the slope between sets of consecutive points. To ensure that the set of all points along this graph is indeed linear. And if those slopes are equal to each other, then indeed it is linear. So, this slope for this segment would be M sub AB. And I'll call the slope between these two consecutive points, M sub BC. So, the idea is we want to test whether M-AB is equal to M-BC. So, let's say that we have coordinates for the different points along this graph. Because the graph of course, had to be generated from a set of data points or a function. In this case, we'll be using a set of data points where the coordinates for point A, for example, will be one comma one. For point B, will be equal to two comma two and for point C, we're going to have three comma three. So, you can probably guess that the slopes are going to be equal. But we're going to prove this. So, M-AB is equal to a change in X divided, sorry, the change in Y divided the change in X. So, in this case, the change in Y is going to be this coordinate point minus this component of the coordinate. So, we have two minus one, divided, same thing, change in X, two minus one. And this is simply equal to one. You do the same for M-BC and we get the change in Y over the change in X as three minus two divided three minus two. Which is also equal to one. So, because all the slopes are equal, then this graph is proportional throughout the extent of the data set. Because of that, we can call this graph linear. My name is Walter Unglaub, and this is how to see if a graph is linear.

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