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.
Step 1. Plug your numbers into the inverse proportion formula
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
If y is 3 when x is 6, what is k ?
Video Answer to Inverse variation problem
Inverse variation graph
When you graph an inverse variation as one quantity increases, the other quantity decreases.
When quantities vary inversely, one quantity increases while the other one decreases.
The values change in opposite directions in an inverse variation, but multiply to a constant, k.
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
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.