# Thread: Help with direct & inverse variations

1. ## Help with direct & inverse variations

I understand the basics of variations, but am having trouble when numbers are applied. For example, I have the following problem:

"Assume that y is directly proportional to x. Use the given x-value and y-value to find a linear model that relates y and x.
x = 9, y = 36 "

How do I find the linear model?

The same goes for this problem:

"Find a mathematical model representing the statement. (In each case, determine the constant of proportionality.) y is inversely proportional to x. (y = 7 when x = 32.)"

Any help is greatly appreciated. Thanks

2. Originally Posted by 305boy
I understand the basics of variations, but am having trouble when numbers are applied. For example, I have the following problem:

"Assume that y is directly proportional to x. Use the given x-value and y-value to find a linear model that relates y and x.
x = 9, y = 36 "

How do I find the linear model?

The same goes for this problem:

"Find a mathematical model representing the statement. (In each case, determine the constant of proportionality.) y is inversely proportional to x. (y = 7 when x = 32.)"

Any help is greatly appreciated. Thanks

Directly proportional means y = k x for some constant k. Plugging in those numbers you get:
36 = k 9

Find k = 4

So the model is y= 4x

Good luck!

3. Originally Posted by 305boy
I understand the basics of variations, but am having trouble when numbers are applied. For example, I have the following problem:

"Assume that y is directly proportional to x. Use the given x-value and y-value to find a linear model that relates y and x.
x = 9, y = 36 "

y is directly proportional to x ... y = kx

y = 4x ... would be a linear equation, right?

The same goes for this problem:

"Find a mathematical model representing the statement. (In each case, determine the constant of proportionality.) y is inversely proportional to x. (y = 7 when x = 32.)"

y is inversely proportional to x ... $\textcolor{red}{y = \frac{k}{x}}$

$\textcolor{red}{y = \frac{224}{x}}$
...