Question

Both relationships represent a direct proportion between x and y. The rate pf change of relationship B is how many unitsgreater than the rate of change of relationship A?

Answer 1

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:

$y=kx$

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:

$y=9x$

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:

$y=kx\to k=\frac{y}{x}$

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:

$\begin{gathered} k=\frac{57.5}{7} \\ k=11.5 \end{gathered}$

The relationship shown on the table follows a direct relationship with the equation

$y=11.5x$

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:

$k_B-k_A=11.5-9=2.5$

The correct option is B