Question
Xin earned $66 at her job when she worked for 4 hours. Fill out a table of equivalent ratios and plot the points on the coordinate axes provided.
Answers
GPT-4o mini
To create equivalent ratios for Xin's earnings, we can start with her initial earning of $66 for working 4 hours. From this information, we can derive ratios of money earned to hours worked.
Let's calculate a few equivalent ratios by finding out how much she would earn for different hours worked:
1. For 1 hour:
\[
\text{Wage per hour} = \frac{66}{4} = 16.5 \text{ (dollars per hour)}
\]
Earnings for 1 hour = $16.5
2. For 2 hours:
\[
2 \text{ hours} = 2 \times 16.5 = 33 \text{ dollars}
\]
3. For 3 hours:
\[
3 \text{ hours} = 3 \times 16.5 = 49.5 \text{ dollars}
\]
4. For 4 hours:
\[
4 \text{ hours} = 66 \text{ dollars}
\]
5. For 5 hours:
\[
5 \text{ hours} = 5 \times 16.5 = 82.5 \text{ dollars}
\]
6. For 6 hours:
\[
6 \text{ hours} = 6 \times 16.5 = 99 \text{ dollars}
\]
Now we have the following equivalent ratios (Earnings in dollars, Hours worked):
| Hours Worked (x) | Earnings (y) |
|------------------|--------------|
| 1 | 16.5 |
| 2 | 33 |
| 3 | 49.5 |
| 4 | 66 |
| 5 | 82.5 |
| 6 | 99 |
### Plotting the Points
To plot the points on the coordinate axes, you would place each point according to the table:
- (1, 16.5)
- (2, 33)
- (3, 49.5)
- (4, 66)
- (5, 82.5)
- (6, 99)
Make sure your y-axis can accommodate values up to 99, and your x-axis can accommodate values up to 6 to fit all points. The points will generally form a straight line since the relationship between hours worked and earnings is linear.
Let's calculate a few equivalent ratios by finding out how much she would earn for different hours worked:
1. For 1 hour:
\[
\text{Wage per hour} = \frac{66}{4} = 16.5 \text{ (dollars per hour)}
\]
Earnings for 1 hour = $16.5
2. For 2 hours:
\[
2 \text{ hours} = 2 \times 16.5 = 33 \text{ dollars}
\]
3. For 3 hours:
\[
3 \text{ hours} = 3 \times 16.5 = 49.5 \text{ dollars}
\]
4. For 4 hours:
\[
4 \text{ hours} = 66 \text{ dollars}
\]
5. For 5 hours:
\[
5 \text{ hours} = 5 \times 16.5 = 82.5 \text{ dollars}
\]
6. For 6 hours:
\[
6 \text{ hours} = 6 \times 16.5 = 99 \text{ dollars}
\]
Now we have the following equivalent ratios (Earnings in dollars, Hours worked):
| Hours Worked (x) | Earnings (y) |
|------------------|--------------|
| 1 | 16.5 |
| 2 | 33 |
| 3 | 49.5 |
| 4 | 66 |
| 5 | 82.5 |
| 6 | 99 |
### Plotting the Points
To plot the points on the coordinate axes, you would place each point according to the table:
- (1, 16.5)
- (2, 33)
- (3, 49.5)
- (4, 66)
- (5, 82.5)
- (6, 99)
Make sure your y-axis can accommodate values up to 99, and your x-axis can accommodate values up to 6 to fit all points. The points will generally form a straight line since the relationship between hours worked and earnings is linear.