Question

a balloon starts at a height of 100 meters and descends at a rate of 5 meters per minute. the function f(x)=-5x+100 gives the balloons height in meters after x minutes. which of the following is the meaning of the y-intercept?

the y-intercept is the initial height of the balloon before it starts descending.

the y-intercept is the time it takes for the balloon to reach the ground.

the y-intercept is the height of the balloon after 20 minutes.

the y-intercept is the time when the balloon is halfway to the ground.

Explanation:

The function is in the slope - intercept form \(y = mx + b\), where \(b\) is the \(y\) - intercept. In the function \(f(x)=-5x + 100\), when \(x = 0\) (before any time has passed, i.e., before the balloon starts descending), \(f(0)=-5\times0+100=100\).

Answer:

The y - intercept is the initial height of the balloon before it starts descending.