Question

charmaine earns $11 an hour at her parttime job. show that the relationship between the amount she earned and the number of hours she worked is a proportional relationship. then write an equation for the relashionship socratic.org socratic.org

Answer 1

Answer:

y = 11 x

Explanation:

The relationship between two variables x,y is said to be a proportional relationship if the ratio between the values of the two variables is constant:

$\frac{y}{x}=k$ (3)

where k is the a constant value valid for all pairs (x,y).

In this problem, we are told that Charmaine earns $11 per hour. Here we call:

y = amount of money earned

x = time

We can see that the relationsip between x and y is proportional. In fact:

- after 1 hour, Charmaine has earned $11 (1)

- after 2 hours, Charmaine has earned $22 (2)

.. and so on

For (1), we find

$\frac{y}{x}=\frac{11}{1}=11$ so k = 11

For (2), we find

$\frac{y}{x}=\frac{22}{2}=11$ so k = 11

So, k = 11 for every pair (x,y), so the two variables have proportional relationship.

Moreover, we can write an equation that relates the two variables re-arranging eq.(3).

$y=kx\\\rightarrow y=11x$