Question

The Wyler Aerial Tramway in Franklin Mountains State Park begins at the tramway station, which is at an elevation of 4692 feet. It takes 4 minutes to reach Ranger Peak, which is at an elevation of 5632 feet. What equation Is used to estimate the height h of the tramway t minutes after it left the station?

Answer 1

Answer:

Let's define x = 0min when the tramway left the station.

We know that the height of the station is 4692 ft.

Then we can define this point as (0min , 4692ft).

And 4 minutes after, the elevation will be 5632ft, then we also have the point

(4min, 5632ft)

Now we can write the height as a function of time with a linear equation:

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

In this case, the slope will be:

a = (5632ft - 4692ft)/(4min - 0min) = 235ft/min

And we already know the value of the y-intercept, this is the value that takes y when x = 0, this is 4692ft.

Then the equation is:

y = (235ft/min)*x + 4692ft

Where:

y = height

x = time in minutes.