2. An airplane travels 780 miles in 4 hours. Make a table and graph to show the mileage for 2,8 , and 12 hours. Is there a direct variation? Explain.

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UpStudy AI · Accepted Answer

To determine if there is a direct variation in the distance traveled by the airplane, we first need to calculate the speed of the airplane and then create a table and graph for the distances traveled over 2, 8, and 12 hours.

### Step 1: Calculate the Speed
The speed of the airplane can be calculated using the formula:

$$
\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{780 \text{ miles}}{4 \text{ hours}} = 195 \text{ miles per hour}
$$

### Step 2: Create a Table
Now, we can create a table showing the distance traveled for 2, 8, and 12 hours.

| Time (hours) | Distance (miles) |
|--------------|-------------------|
| 2            | $$ 195 \times 2 = 390 $$ |
| 8            | $$ 195 \times 8 = 1560 $$ |
| 12           | $$ 195 \times 12 = 2340 $$ |

So the completed table is:

| Time (hours) | Distance (miles) |
|--------------|-------------------|
| 2            | 390               |
| 8            | 1560              |
| 12           | 2340              |

### Step 3: Graph the Data
To graph the data, you can plot the points (2, 390), (8, 1560), and (12, 2340) on a coordinate plane where the x-axis represents time in hours and the y-axis represents distance in miles.

### Step 4: Determine Direct Variation
A relationship is said to have direct variation if it can be expressed in the form $$ y = kx $$, where $$ k $$ is a constant. In this case, the distance $$ y $$ is directly proportional to the time $$ x $$ with a constant speed of 195 miles per hour.

Since the distance increases linearly with time, we can conclude that there is a direct variation. The constant of variation $$ k $$ is 195 miles per hour.

### Conclusion
Yes, there is a direct variation in the distance traveled by the airplane with respect to time, as the distance can be expressed as $$ \text{Distance} = 195 \times \text{Time} $$.
The airplane's speed is 195 miles per hour. The table shows distances for 2, 8, and 12 hours: 390, 1560, and 2340 miles, respectively. The graph of these points shows a direct variation, as the distance is directly proportional to the time.

2. An airplane travels 780 miles in 4 hours. Make a table and graph to show the mileage for 2,8 , and 12 hours. Is there a direct variation? Explain.

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