Question

The graph shown here displays the distance, in miles, traveled by an airplane in a certain number of hours. Based on the graph, which of the following equations indicates the correct variables, and in how many hours does the airplane travel 8,000 miles if it travels at the same speed?

A.x = 200y, the airplane travels 8,000 miles in 42 hours
B.y = 200x, the airplane travels 8,000 miles in 42 hours
C.x = 200y, the airplane travels 8,000 miles in 40 hours
D.y = 200x, the airplane travels 8,000 miles in 40 hours

Answer 1

We first need to set up an equation.
Let's do y÷x with one of the points.
Let's use (4,800)
800×4=200
So, the equation is 200x=y
Let's look at what they're asking us.
How many hours does it take for a plane to travel 8,000 miles?
We could solve this two ways. One by multiplying a value that's already on the graph or by using the equation.
You can plug in 8,000 for y.
200x=8,000
Divide.
8,000÷200=40
So, it takes 40 hours.
The other way to do this is to look at how it takes 4 hours to travel 800 miles.
We need 10 times those miles, to multiply the hours by 10, you ge 40 hours as well.
D. y=200x; the airplane travles 8,000 miles in 40 hours.

Answer 2

You can see on the graph that (x, y) = (2, 400) is one of the points the line goes through. That is, y = 200x. Then for x=40, y = 200·40 = 8000.

The appropriate choice is
D. y = 200x, the airplane travels 8000 miles in 40 hours