Respuesta :
A direct relationship between two variables x and y occur when the variable y grows proportionally with x, you can express a direct relationship as follows:
[tex]y=kx[/tex]Where k is the constant of proportionality and indicates the increase of y for every unit increase of x.
Relationship A
This is represented by the equation:
[tex]y=9x[/tex]This equation shows that every time the variable "x" increases one unit, the variable "y" increases k=9 units. This is a direct relationship between both variables.
Relationship B
To determine the constant proportionality of the relationship shown on the table, you can write the expression that shows a direct relationship for k:
[tex]y=kx\to k=\frac{y}{x}[/tex]Choose one ordered pair from the table, for example (5,57.5), and replace the values of x and y on the expression to determine the constant of proportionality:
[tex]\begin{gathered} k=\frac{57.5}{7} \\ k=11.5 \end{gathered}[/tex]The relationship shown on the table follows a direct relationship with the equation
[tex]y=11.5x[/tex]The rate of change, or constant of proportionality, of the relationship A is k=9, and the rate of change of B is k=11.5, to determine how many units greater the change of rate of B is, with respect to A, you have to calculate the difference between both values:
[tex]k_B-k_A=11.5-9=2.5[/tex]The correct option is B
