Direct Variation | Constant of Variation | MathHelp.com - By MathHelp.com
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| 00:00 | if why varies directly as X and Y equals six | |
| 00:05 | . When X equals four , find K the constant | |
| 00:10 | of variation , write an equation that represents the relationship | |
| 00:16 | between X and Y . Find why when x equals | |
| 00:21 | seven And find x when y equals 12 . Let's | |
| 00:27 | start with the first part of the problem . If | |
| 00:31 | why varies directly is X and Y equals six . | |
| 00:36 | When X equals four , find K . The constant | |
| 00:41 | of variation . We know that . If why varies | |
| 00:45 | directly as X . Then we can use the formula | |
| 00:49 | Why equals K . X . Mhm . And were | |
| 00:56 | given that y equals six when x equals four . | |
| 01:01 | So we can substitute these values into our formula for | |
| 01:06 | X and Y . To get six equals K times | |
| 01:12 | four . Now to solve for K , we divide | |
| 01:17 | both sides of the equation by four And we find | |
| 01:22 | that 1.5 equals K . Next we're asked to write | |
| 01:32 | an equation that represents the relationship between X and Y | |
| 01:38 | . Since we know that K are constant of variation | |
| 01:43 | is 1.5 . We simply plug a 15 back into | |
| 01:49 | our direct variation formula for K . And we have | |
| 01:55 | y equals 1.5 x . Mhm . Next we're asked | |
| 02:05 | to find why when x equals seven . Yes . | |
| 02:14 | So using our equation why equals 1.5 x . We | |
| 02:25 | substitute a seven in for X . And we have | |
| 02:32 | y equals 1.5 times seven , Or y equals 10.5 | |
| 02:43 | . Yeah . Yeah . Finally we're asked to find | |
| 02:50 | x when y equals 12 . Yeah . Yes . | |
| 02:57 | So using our equation y equals 1.5 x . We | |
| 03:07 | substitute a 12 in for why ? Mhm . Yeah | |
| 03:12 | . And we have 12 equals 1.5 x . And | |
| 03:19 | dividing both sides by 1.5 . We find that A | |
| 03:28 | equals X . Yeah . |
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