Question

= table shows a hot air balloon's height h, in feet, during a descent at various times t, in seconds.
Time Height
(seconds) (feet)
5
1150
10
1090
15
1030
20
970
25
910
at air balloon's initial rate of change (slope).

Answer 1

Answer:

A. Slope is -12 feet per second

B. Yes, it is constant.

Skills needed: Linear Equations, Substitution and Division

Step-by-step explanation:

1) Solving Part A (we need to find the slope):

• The slope is $\frac{y_2-y_1}{x_2-x_1}$ --> $y_1$, $y_2$, $x_1$, and $x_2$ are all values from the table. We know that the left column is the x-values, and the right column is the y-values as that is the conventional way of depicting them.

2) Using the y-values of 1150 and 1090, and their corresponding x-values (5 and 10 respectively), we can get the slope:

- $\frac{y_2-y_1}{x_2-x_1}$ ==> $\frac{1090-1150}{10-5}$ ==> $1090-1150=-60, 10-5=5$ ==> $\frac{-60}{5}$

$\frac{-60}{5} =-12$, so the slope is -12.

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1) Part B (analysis)

We can see that no matter what 2 y-values and their corresponding x values we use, the slope always is the same. This means that the rate of change is constant.