How to Graph a Direct Variation That Includes Given Points

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Graphing a direct variation that includes given points is something that you can do with the X and Y plane. Graph a direct variation that includes given points 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 graph a direct variation that includes given points. So if we're given three points let's say point A with coordinates zero, zero, point B with coordinates one, two and point C with coordinates two, four. We can look to the x, y plane and plot these points. So I have point A over here at the origin and then point B over here where x is one and y is two. And finally point C located here. So a direct variation essentially implies that there's a linear relationship between the x and the y coordinates. So if I connect these three points I end up with a straight line and I can characterize this using the slope intercept equation which is y is equal to mx plus b where b is the y intercept. In this case it's zero. And I can calculate m by considering the change in y over the change in x using the given data points. So if I consider for example C and B I have y of C minus y of B divided by x of C minus x of B. And this is simply going to be equal to four minus two divided by two minus one which is equal to two over one or simply two. So I have a line here that I'm graphing that's equal to y is equal to two x where my slope is two and I have a direct variation. So two which is the slope is sometimes called the constant of proportionality. Meaning that y is proportional to x but with a factor of two. My name is Walter Unglaub and this is how to graph a direct variation with given points.


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