your grade, g, on a test vaires directly with the number of hours, n, that you study for it.

Question

please help me write this problem in a general formula that describe these variations, using k as the constant of proportionality

 

Answer 1

A "direct" variation is a simple relationship in which the value of one variable changes in direct proportion to the changes in another variable. Generically, we would say "y" varies proportionally (or directly) as "x" varies.

 

"X" is usually the variable you control, and "Y" is the variable that responds to changes you make in "X."

 

The form of the equation is this:   Y = Kx

 

A fairly common example is employment. If you earn, say, $5 and hour, then the relationship between the hours you work, and the amount of money you earn, would look like this:    Y = 5X

 

But it is better to use letters that make sense for a particular context, so let's write:     P = 5H, where

 

P = pay

H = hours worked.

 

This function turns time into money!

 

In this example, "5" is the constant of proportionality. In other words, for this problem, K = $5/hr.

 

So, we write, P = 5H.

 

If you get a raise, then the value of "K" increases, and you make more money, more quickly!

 

You get a raise to $10/hr, then the formula becomes this:    P = 10H .

 

We say, "P varies directly with the number of hours, H, that you work."

 

Now you try it!

:PC