example of a linear equation that is a direct variation....
y = 3 x
not
y = 3x + 1
That is linear but not direct
not
y= 3x^2
That is direct but not linear
thanks
Sure! A linear equation that exhibits direct variation represents a relationship between two variables where one variable is a constant multiple of the other. In other words, as one variable increases or decreases, the other variable changes proportionally.
To create an example of a linear equation that is a direct variation, you need to express the relationship between the variables using the format y = kx, where "k" is the constant of variation.
Let's say we have a situation in which the variable "y" represents the cost of buying "x" number of apples, and we want to show that the cost of apples is directly proportional to the number of apples bought.
We can set the constant of variation as the cost of a single apple, and express this relationship as:
y = 2x,
where "y" represents the cost of buying "x" number of apples, and "2" is the constant of variation.
In this example, as the number of apples purchased increases by 1, the cost also increases by a factor of 2.
This equation represents a linear equation with direct variation because the variables "y" and "x" are related proportionally, and the equation follows the form y = kx.