Question

What's the C.O.P? I don't know how to solve it

Answer 1

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:

`(\text{ x , y ) - > ( 16 , 216 )}`

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:

`y\text{ = k}\cdot x`

Where,

`k\colon\text{ Constant of proportionality}`

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:

`\begin{gathered} k\text{ = }(y)/(x) \\ \\ k\text{ = }(216)/(16) \\ \\ k\text{ = 13.5} \end{gathered}`

We plugged in the respective quantities of the variables ( x ) and ( y ) and evaluated for the constant of proportionality ( k ):

`COP\text{ = 13.5 }\ldots\text{ Answer}`