Question

A group of climbers begin climbing at an elevation of 5000 feet and ascend at a steady rate of 1500 vertical feet per hour. This situation can be modeled by a linear function. Identify the independent and dependent variables.

Answer 1

Linear function:
`y=1500x+5000`

x- Independent variable

y- Dependent variable

Explanation:

We are given that

Climbers start climbing at an elevation of height =5000 ft

The steady rate at which climbers start climbing=1500 ft/h

We have to find the independent variable and dependent variable.

Let time taken by climbers=x hours

In 1 hour, climbers cover distance =1500 ft

In x hours , climber cover distance=1500x ft

According to question

The total distance y covered by climber in x hours

`y=1500x+5000`

This is required linear function.

We can see that

x does not depend on any other quantity.Therefore, x is independent variable .

When the value of x changes then the value of y is also change.

It means the value of y depends on the value of x.

Therefore, y is dependent variable.