What is the direct variation function?
Is it y/x=k?
Yes, the direct variation function is commonly expressed as y = kx, where y and x represent variables and k is a constant. This equation signifies that y and x are directly proportional to each other.
To understand why the direct variation function is y = kx, let's break it down:
- The letter "y" represents the dependent variable, or the variable that is being influenced or affected by another variable.
- The letter "x" represents the independent variable, or the variable that influences or affects the dependent variable.
- The constant "k" is the proportionality constant, which maintains the relationship between y and x.
To determine the value of k in a specific problem, you need to have at least one set of values for y and x. Once you have that, divide the value of y by the value of x to find k. Then, you can formulate the equation y = kx.
For example, if you have a set of values such as (2, 5) and (4, 10), you can calculate k as follows:
k = y/x = 5/2 = 10/4 = 2.5
With k = 2.5, the direct variation function for this example would be y = 2.5x.