Question

A hot air balloon is currently at a height of 900 feet. The balloon is descending by 10 feet minute. Find a function for the balloon's height after x minutes

Answer 1

`y=-10x+900`

Explanation:

Let

x -----> the number of minutes

y ----> the balloon's height in feet

we know that

The linear equation in slope intercept form is equal to

`y=mx+b`

where

m is the slope

b is the y-coordinate of the y-intercept

In this problem we have that

The slope is equal to

`m=-10\ (ft)/(min)` ----> is negative because is a decreasing function

`b=900\ ft`

Remember that the y-intercept is the value of y when the value of x is equal to zero

In this context the y-intercept is the height of the balloon when the time is equal to zero (initial height)

substitute

`y=-10x+900`