We are asked to make a table and a graph to show the mileage of an airplane for 2, 8, and 12 hours.
Let's start by finding how far the airplane travels in 1 hour. We know that the plane travels 780 miles in 4 hours. Let's write a ratio to show this situation.
780miles/4hours
To find how many miles the airplane travels in 1 hour, we will write an equivalent rate with a denominator of 1 hour. Let's ignore the units for now to keep our calculations simple.
We found the unit rate of the airplane's speed.
780miles/4hours = 195miles/1hour
As we can see, the airplane travels at 195 miles per hour. We can use this information to make a table to show the mileage for 2, 8, and 12 hours.
Hours
2
8
12
Miles
195(2)=390
195(8)=1560
195(12)=2340
Now we want to make a graph with this data. We will start by writing the two quantities as ordered pairs where the x-coordinate is the number of hours and the y-coordinate is the number of miles.
Finally, let's connect the ordered pairs and extend the line to the y-axis.
As a last step, we want to determine whether the given relationship is a direct variation. Recall that the relationship of two variable quantities is a direct variation if it has a constant ratio. In this case, the ratio of miles to hours is 195 miles per hour and is constant. This means that the given relationship is a direct variation.
