Definition inverse variation

k = The constant of proportionality

x = x coordinate

y = y coordinate

The time traveling varies inversely to the speed of your car. The faster you travel, the less time it takes you to arrive. If you travel 8 hours at 50 miles per hour, find the constant of proportionality.

Then find the speed you must travel to arrive in 6 hours.

x

y =

Step 1. Plug your numbers into the inverse proportion formula

3= k/6

Step 2. Place a 1 under 3 and then perform a cross product.

Step 3. k= 18

Step 4. Plug the k into your original formua

y = __18__

x

When you graph an inverse variation as** one quantity** increases, the other **quantity** decreases.

1

2

3

4

y

x

6

3

2

3/2

To see if a relation is inversely proportional, multiply x and y together. If each ordered pair multiplies to the same constant then it IS an inverse proportion.

ex. (1, 6) 1 x 6 = 6 (2, 3) 2 x 3 = 6 (3, 2) 3 x 2 = 6 (4, 3/2) 4 x 3/2 = 6

Transcript
Inverse Variation
Today we are going to look at inverse variation. Inverse variation is when Y varies inversely with X. Here is our example. If Y is three and X is six, what is K? Well first of all we need to know an equation. So here are the rules that go along with inverse variation. Y is equal to K over X . If I place a one underneath this Y I would have the Y on the top of the fraction and X on the bottom,so our variables are one on top and one on bottom of our fraction. So it’s kind of like a portion with a variable on each end and then we solve for K by plugging in our X and Y and multiplying our Y times X and X times Y and then we will take that K and plug it into the original equation. Y equals K over X with Y and X being the generic variables and we will plug the K that we are going to solve for. Let’s walk through this example. If Y is equal to three and X is six what is K? First, let’s write our equation down. Y equals K over X If Y is three, I’ll plug in three for Y and X is six then I’m plug in six for X and I will leave K as our unknown because we don’t know what K is. Place a one under three because that is a whole number, and a whole number always has a one. Next I’m going to do a cross multiplication or cross product. Three times six is eighteen times one is just K so the value for K is eighteen. Now let’s go back and plug it into the original equation leaving X and Y as variables and just plugging K in. My final equation is Y equals eighteen over X and that’s how you would write the inverse for that problem. Hope this helps.