Algebra Functions Direct and inverse variation Direct and Inverse Variation Recognizing Direct and Inverse Variation Proportionality Constant for Direct Variation Direct and inverse variation Direct Variation Models Direct Variation 1 Inverse Variation Application Direct Inverse and Joint Variation Direct Variation Application Direct Variation 1 Direct Variation 1 Practice this concept Back Direct Variation 1 ⇐ Use this menu to view and help create subtitles for this video in many different languages. You'll probably want to hide YouTube's captions if using these subtitles. We're told that the total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing. So this first statement tells us that if x is equal to the number of gallons purchased, and y is equal to the cost of filling up the car, this first statement tells us that y varies directly with the number of gallons, with x. So that means that y is equal to some constant, we'll just call that k, times x. This is what it means to vary directly. If x goes up, y will go up. We don't know what the rate is. k tells us the rate. If x goes down, y will be down. Now, they give us more information, and this will help us figure out what k is. If a gallon of gas costs $2.25, how many gallons could you purchase for $18? So if x is equal to 1-- this statement up here, a gallon of gas-- that tells us if we get 1 gallon, if x is equal to 1, then y is $2.25, right? y is what it costs. They tell us 1 gallon costs $2.25, so you could write it right here, $2.25 is equal to k times x, times 1. Well, I didn't even have to write the times 1 there. It's essentially telling us exactly what the rate is, what k is. We don't even have to write that 1 there. k is equal to 2.25. That's what this told us right there. So the equation, how y varies with x, is y is equal to 2.25x, where x is the number of gallons we purchase. y is the cost of that purchase, so it's $2.25 a gallon. And then they ask us, how many gallons could you purchase for $18? So $18 is going to be our total cost. It is y cost of filling the car. So 18 is going to be equal to 2.25x. Now if we want to solve for x, we can divide both sides by 2.25, so let's do that. You divide 18 by 2.25, divide 2.25x by 2.25, and what do we get? Let me scroll down a little bit. The right-hand side, the 2.25's cancel out, you get x. And then what is 18 divided by 2.25? So let me write this down. So first of all, I just like to think of it as a fraction. 2.25 is the same thing-- let me write over here-- 2.25 is equal to 2 and 1/4, which is the same thing as 9 over 4. So 18 divided by 2.25 is equal to 18 divided by 9 over 4, which is equal to 18 times 4 over 9, or 18 over 1 times 4 over 9. And let's see, 18 divided by 9 is 2, 9 divided by 9 is 1. That simplifies pretty nicely into 8. So 18 divided by 2.25 is 8, so we can buy 8 gallons for $18. Questions Tips & Feedback Be specific, and indicate a time in the video: At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger? Have something that's not a question about this content? Post a tip or feedback General discussion about the site Report a technical problem with the site Request a video or feature This discussion area is not meant for answering homework questions. Formatting tips Cancel or ( total) Share a tip When naming a variable, it is okay to use most letters, but some are reserved, like 'e', which represents the value 2.7831... Suggest a fix At 2:33, Sal says "double bonds" but should say "single bonds." Have something that's not a tip or feedback about this content? Ask a question General discussion about the site Report a technical problem with the site Request a video or feature This discussion area is not meant for answering homework questions. Formatting tips Cancel or Discuss the site For general discussions about Khan Academy, visit our Reddit discussion page. Flag inappropriate posts Here are posts to avoid making. If you do encounter them, flag them for attention from our Guardians. abuse disrespectful or offensive an advertisement not helpful low quality not about the video topic soliciting votes or seeking badges a homework question a duplicate answer repeatedly making the same post wrong category a tip or feedback in Questions a question in Tips & Feedback an answer that should be its own question about the site a question about Khan Academy (Visit our FAQ) a post about badges a technical problem with the site (Report a problem) a request for videos or features
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