Geraldo gets paid the same amount for each hour he works. The graph shows the amount he is paid, y, as it relates to the number of hours he works, x. Yesterday, when he worked 6 hours, he was paid $84.

Question

Geraldo’s Earnings
On a coordinate plane, a graph titled Geraldo's Earnings has number of hours on the x-axis and wages in dollars on the y-axis. The line goes through points (0, 0) and (6, 84).

Which ordered pair could represent the number of hours and amount Geraldo is paid today at the same hourly wage?
(3, 42)
(4, 60)
(5, 62)
(8, 100)

Answer 1

To determine Geraldo’s hourly wage, we can use the information given about his payment for 6 hours of work. Since he earned $84 for 6 hours, we can calculate his hourly wage:

\[ \text{Hourly Wage} = \frac{\text{Total Earnings}}{\text{Total Hours Worked}} = \frac{84}{6} = 14 \text{ dollars per hour} \]

Now, we can use this hourly wage to find out how much he would earn for different numbers of hours worked. The earnings \(y\) for any number of hours worked \(x\) can be expressed with the equation:

\[ y = 14x \]

Now we can calculate the earnings for each of the ordered pairs provided:

1. For (3, 42): \[ y = 14 \times 3 = 42 \] This pair is valid.

2. For (4, 60): \[ y = 14 \times 4 = 56 \] This pair is not valid.

3. For (5, 62): \[ y = 14 \times 5 = 70 \] This pair is not valid.

4. For (8, 100): \[ y = 14 \times 8 = 112 \] This pair is not valid.

Based on these calculations, the only ordered pair that could represent the number of hours and amount Geraldo is paid today at the same hourly wage is:

\[ \boxed{(3, 42)} \]