Question

while being deflated, a hot - air balloon loses 300 cubic meters of air every 3 minutes. after 6 minutes, the balloon has 900 cubic meters of air. the volume of the air in cubic meters, y, is a function of the time in minutes, x. rate of change: - 100 point on the graph: (6, 900) initial value: 1,500 y = mx + b (rate of change, initial value) write the equation of the function.

Explanation:

Step1: Identify the slope-intercept form

The general form of a linear function is \( y = mx + b \), where \( m \) is the rate of change (slope) and \( b \) is the initial value (y-intercept).

Step2: Substitute the given values

We know the rate of change \( m = -100 \) and the initial value \( b = 1500 \). Substituting these into the slope-intercept form, we get \( y = -100x + 1500 \).

Answer:

\( y = -100x + 1500 \)