Question

1. given the table, determine whether the amount of money earned is proportional to the number of hours worked. if so, calculate the constant of proportionality and explain what it means in this situation.

time worked (hours)	money earned (dollars)
4	26
5.5	35.75
10	65

Explanation:

Step1: Check proportionality

For two - variables $x$ (time worked) and $y$ (money earned) to be proportional, the ratio $\frac{y}{x}$ should be constant.
For the first row: $\frac{3.25}{0.5}=\frac{325}{50} = 6.5$
For the second row: $\frac{26}{4}=\frac{13}{2}=6.5$
For the third row: $\frac{35.75}{5.5}=\frac{3575}{550}=\frac{143}{22}=6.5$
For the fourth row: $\frac{65}{10}=6.5$
Since $\frac{y}{x}$ is constant for all rows, the amount of money earned is proportional to the number of hours worked.

Step2: Determine the constant of proportionality

The constant of proportionality $k$ is the ratio of money earned to time worked. As calculated above, $k = 6.5$.

Step3: Explain the meaning

The constant of proportionality $k = 6.5$ means that for every 1 hour of work, the amount of money earned is $6.5$ dollars.

Answer:

The amount of money earned is proportional to the number of hours worked. The constant of proportionality is $6.5$, which means the hourly wage is $6.5$ dollars per hour.