According to the given data, we determined that y does vary directly with respect to x according to the following relationship: [tex]y=1.6 \cdot x[/tex].
On this problem, we have 2 variables x and y, variables are states or numbers which are not constant over time. According to the situation, variables can be related or unrelated:
In case 2 variables are related, then there exists a function which relates both of them. That function can be of any type (polynomial, trigonometric, logarithmic, a mixture of them, etc.), and they all have their unique form. Direct variation is the simplest of them because, taking our variables x and y as an example, we can write that [tex]y=c\cdot x[/tex], where c is called the proportionality constant.
The solution to this problem is to find constant c and check if it is unique for all the given data points [tex](4,6.4)\ ; (7,11.2)\ ; (10,16)\ ; (13,20.8)[/tex]. We can find constant c for all the data points as [tex]c=\frac{y}{x}[/tex], doing the math we get:
[tex]c=\frac{6.4}{4} = 1.6[/tex]
[tex]c=\frac{11.2}{7} = 1.6[/tex]
[tex]c=\frac{16}{10} = 1.6[/tex]
[tex]c=\frac{20.8}{13} = 1.6[/tex]
Since all the encountered values of c are the same we can say that both variables are directly related by the equation [tex]y=c\cdot x[/tex]
Direct variation, variable, relation with respect to.
