What is constant of variation

Video transcript y is directly proportional to x. If y equals 30 when x is equal to 6, find the value of x when y is So let's just take this each statement at a time.

That's literally just saying that y is equal to some constant times x. This statement can literally be translated to y is equal to some constant times x. Now, they tell us, if y is 30 when x is and we have this constant of proportionality-- this second statement right over here allows us to solve for this constant.

When x is 6, they tell us y is 30 so we can figure out what this constant is. We can divide both sides by 6 and we get this left-hand side is 30 divided by 6 is 5.

If you drive at 30 mph and it takes you 5 hours to reach your destination, how fast do you have to drive to reach your destination in 30 minutes. First, let's find k, the constant of proportionality.

We can use that to find k. Algebra 1 Direct vs. Inverse Variation. Go to Topic. Explanations 3 Alex Federspiel. Video Inverse Variation by mathman Here's a video by mathman explaining inverse variation or inverse proportionality. Show Solution Check. Related Lessons. View All Related Lessons. Alex Federspiel. What are Inverse Proportions?

Is this an inversely proportional equation? Example: Using Tables Sometimes you'll be given a table and have to figure out if its inversely proportional or not. Example: Word Problems The general steps to solving these proportionality problems are: Use the given information to find k. Use k to find the unknown information. Let's look at an example: The time, t, it takes to paint a house varies inversely with the number of people painting, p. Practice Problem The time it takes to complete a drive is inversely proportional to the speed at which you drive.

In these equations, the output equals a constant divided by the input variable that is changing. One example of an inverse variation is the speed required to travel between two cities in a given amount of time. The more time you have, the slower you can go. Water temperature is inversely proportional to depth in the ocean. The water temperature in the ocean varies inversely with the depth of the water.

The deeper a person dives, the colder the water becomes. You are told that this is an inverse relationship and that the water temperature y varies inversely with the depth of the water x. A third type of variation is called joint variation. Joint variation is the same as direct variation except there are two or more quantities. If you change the width of the rectangle, then the area changes and similarly if you change the length of the rectangle then the area will also change.

The volume of the cylinder varies jointly with the square of the radius and the height of the cylinder. The area of a triangle varies jointly with the lengths of its base and height. You are told that this is a joint variation relationship and that the area of a triangle A varies jointly with the lengths of the base b and height h. In the following video, we show an example of finding the constant of variation for a jointly varying relation.

Rational formulas can be used to solve a variety of problems that involve rates, times, and work.