Question

a hot air balloon rose at a constant rate. after 3 minutes, the balloon was 44 meters above the ground. then, 2 minutes later, the hot air balloon had risen to 70 meters above the ground.
how much did the hot air balloon rise each minute?
\boxed{} meters
how far above the ground was the hot air balloon at the start of the ride?
\boxed{} meters
complete the equation that describes the relationship between the altitude of the hot air balloon in meters, a, and the elapsed time in minutes, t.
write your answer using whole numbers or decimals rounded to the nearest tenth.
a = \boxed{} t + \boxed{}

Explanation:

Step1: Find the rate of rise (slope)

The balloon rises from 44 meters to 70 meters in 2 minutes. The change in altitude is $70 - 44 = 26$ meters, and the change in time is 2 minutes. So the rate $m$ is $\frac{26}{2}=13$ meters per minute.

Step2: Find the initial altitude (y-intercept)

Using the point (3, 44) and the slope $m = 13$ in the equation $A = mt + b$. Substitute $t = 3$, $A = 44$, and $m = 13$: $44 = 13\times3 + b$. Calculate $13\times3 = 39$, then $b = 44 - 39 = 5$ meters.

Step3: Write the equation

Using $m = 13$ and $b = 5$, the equation is $A = 13t + 5$.

Answer:

13
5
13, 5 (for the equation \( A = 13t + 5 \))