Question

1. the table below shows the height $h$ (in feet) of a hot air balloon $t$ minutes after it takes off from the ground. it rises at a constant rate.

$t$ (minutes) | $h$ (feet)
--- | ---
2 | 300
5 | 750
9 | 1,350

equation:
use the table and equation to tell the story of the hot air balloon.

Explanation:

Step1: Find the constant rate

$\text{Rate} = \frac{750 - 300}{5 - 2} = \frac{450}{3} = 150$ feet per minute

Step2: Verify the rate

$\text{Check with 9 minutes: } 150 \times 9 = 1350$, which matches the table.

Step3: Write the linear equation

Since the balloon starts at ground level (height 0 at $t=0$), the equation is $h = 150t$.

Answer:

Equation:

$h = 150t$

Story:

A hot air balloon takes off from ground level and rises at a constant speed of 150 feet per minute. After 2 minutes, it reaches a height of 300 feet; after 5 minutes, it is at 750 feet; and by the 9th minute, it has ascended to 1350 feet above the ground.