Question

Exercise 6. A passenger's tram ride from to Sandia Peak begins at an elevation of 6559 feet. One minuteafter starting the passenger is at 6814 feet.(a) Find a linear function for the passenger's elevation, h, in feet, t minutes after starting the ride.(b) Give the units and practical interpretations of the slope and vertical intercept

Answer 1

We can express the location of the passener as a point (t, h)

where t is the time passes in minutes

and h is the height or elevation in feet

The first point is when time is 0 min and the starting elevation is 6559 feet.

So this will be the first point (0, 6559)

The next point is after 1 minute which has an elevation of 6814 feet.

So the second point will be (1, 6814)

Note that the equation of the line formed between two points can be determine using two-point formula.

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

where x1, y1 are the coordinates of the first point

and x2 y2 are the coordinates of the second point

Substitute the given values to the formula :

`\begin{gathered} y-6559=(6814-6559)/(1-0)(x-0) \\ y-6559=255x \\ y=255x+6559 \end{gathered}`

Now replace the variables, x to t, and y to h

a. The linear function will be :

`h=255t+6559`

b. the slope and the vertical intercept :

Note that if the line is in the form of :

`y=mx+b`

m is the slope and b is the y-intercept or vertical intercept.

From the linear function we have.

the slope is 255

and the vertical intercept is 6559

The slope of 255 means that the elevation is increasing at a rate of 255 feet per minute

and the vertical intercept means that this is the starting elevation at time = 0.

The starting elevation is 6559 feet