We will investigate how to determine the constant of proportionality for specific relationship between two variables.
We are given the respect proportionality between two variables ( x and y ) on a cartesian coordinate plane as such:
[tex](\text{ x , y ) - > ( 16 , 216 )}[/tex]
We are to determine the constant of proportionality ( k ) for the relationship expressed between the two variables.
A general proportional relation between ( x ) and ( y ) is expressed as follows:
[tex]y\text{ = k}\cdot x[/tex]
Where,
[tex]k\colon\text{ Constant of proportionality}[/tex]
We will use the given data point ( x , y ) and the general expression for direct proportions to determine the value of the constant of proportionality ( k ) as follows:
[tex]\begin{gathered} k\text{ = }\frac{y}{x} \\ \\ k\text{ = }\frac{216}{16} \\ \\ k\text{ = 13.5} \end{gathered}[/tex]
We plugged in the respective quantities of the variables ( x ) and ( y ) and evaluated for the constant of proportionality ( k ):
[tex]COP\text{ = 13.5 }\ldots\text{ Answer}[/tex]
