Question

The amount Lins sister earns at her part time job is proportional to the number of hours she works. She earns 9.60 dollars per hour1. Write an equation in the form y=kx to describe this situation, where x represents the hours she works and y represents the dollars she earns.2. is y a function of x? explain how you know.3. Write an equation describing x as a function of y

Answer 1

The amount Lins sister earns at her part-time job is proportional to the number of hours she works.

She earns 9.60 dollars per hour.

1. Write an equation in the form y=kx to describe this situation, where x represents the hours she works and y represents the dollars she earns.

$9.60 per hour means that y = 9.60 and x = 1

`\begin{gathered} y=kx \\ 9.60=k(1) \\ k=(9.60)/(1) \\ k=9.60 \end{gathered}`

Since we found the value of constant k, so the relation becomes

`y=9.60x`

2. is y a function of x? explain how you know

y is a function of x means that the value of y depends on the value of x.

In the above function, when the value of x changes then the value of y will also change.

3. Write an equation describing x as a function of y​

To write the equation describing x as a function of y, make x the subject of the equation.

This simply means to separate out the variable x.

`\begin{gathered} y=9.60x \\ 9.60x=y \\ x=(y)/(9.60) \end{gathered}`