I need help writing the rule. I thought would be just y=kx

Earning $4.23 for each half hour rate that i work. How much money do i earn during a given amount of time?

it is.

You can define x as the number of half-hours that you work. In that case, y = 4.23x

Or, you can define x as the number of hours that you work.
In that case it is twice as many as the number of 1/2-hours that you work, right? So, y = 4.23(2x) = 8.46x

actually, I worded the 2nd part wrong. If x is the number of 1/2-hours, then each hour is two 1/2-hours.

Or, you can convert hours to dollars if you watch the units. For x hours, you have

4.23 $/half-hour * 2 half-hour/hour = 8.46 $/hr * x hr = $8.46x

Thank you Steve for explaining it to me great help

To find out how much money you will earn during a given amount of time, you can use the equation y = kx, where y represents the amount of money earned, k represents the earning rate per unit of time, and x represents the amount of time worked.

In this case, your earning rate is $4.23 per half hour, which means k = $4.23.

Let's say you want to find out how much money you will earn during 3 hours. To do this, you need to convert the given time into the same units as the earning rate. Since the earning rate is in half hours, we need to convert 3 hours to half hours.

1 hour = 2 half hours

Therefore, 3 hours = 3 * 2 = 6 half hours. Now we can substitute this value into the equation.

y = kx
y = $4.23 * 6

By multiplying the earning rate per half hour ($4.23) by the number of half hours worked (6), you will find the amount of money earned.

y = $4.23 * 6
y = $25.38

So, you will earn $25.38 during 3 hours of work.