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Direct Variation - Concept
MA, Stanford University
Teaching in the San Francisco Bay Area
Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts
We often use the term direct variation to describe a form of dependence of one variable on another. An equation that makes a line and crosses the origin is a form of direct variation, where the magnitude of x increases or decreases directly as y increases or decreases. Direct variation and inverse variation are used often in science when modeling activity, such as speed or velocity.
There's a special kind of relationship in math that's called Direct Variation. We say that two vari- two variables very directly if they fit this equation y=kx. Where we call the k the constant of variation.
Pretty much what this means is that you have an equation that passes through the point 00 and here's why I tell you that. Remember you guys are already familiar with y=mx+b, this is really really similar the only thing is I'm taking away the b or making into 0. Instead of the letter m I'm using the letter k.
Direct variation is just a slight completely different version of what you guys already know about y=mx+b equations. So when you're doing these kinds of problems keep in mind that your y intercept is always going to be 0. You can also keep in mind that these lines will contain the point 00. So if ever you're asked to write an equation or to interpret the slope or something or like like that you can use the point 00 along with either your slope intercept form of an equation or your point slope form.
So before you guys try these problems couple of things to keep in mind just to remind or just to keep in the back of your head direct variation equations always look like y equals some number times x. And they're just like y=mx+b equations only instead of m you're calling that value k, and your b value is always going to be 0.
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Sample Problems (5)
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Problem 1 8,326 views
If y varies directly with x and the value of y is 22 when the value of x is 2, find y when x = 5.
Problem 2 4,973 views
A biker's distance traveled on flat terrain varies directly with its traveling time. If the biker has gone 90 miles after 2½ hours, how long will it take him to go 306 miles?
Problem 3 322 views
Problem 4 308 views
Problem 5 297 views