Question

scientists are measuring a distant planets temperature. the graph shows the temperature (in °c) versus the height (in kilometers) above the planets surface. (a) what is the temperature at 0 kilometers? °c (b) choose the statement that best describes how the height and temperature are related. then fill in the blank. as the height increases, the temperature decreases. as the height increases, the temperature increases. at what rate is the temperature decreasing? °c per kilometer at what rate is the temperature increasing? °c per kilometer

Explanation:

Step1: Find temperature at 0 kilometers

From the graph, when height = 0 kilometers, the temperature is - 3°C.

Step2: Determine relationship between height and temperature

The graph is a straight - line with a positive slope. So, as the height increases, the temperature increases.

Step3: Calculate the rate of change

We can choose two points on the line, say (0, - 3) and (36, 3). The rate of change (slope) $m=\frac{y_2 - y_1}{x_2 - x_1}$, where $x_1 = 0,y_1=-3,x_2 = 36,y_2 = 3$. Then $m=\frac{3-(-3)}{36 - 0}=\frac{6}{36}=\frac{1}{6}$ °C per kilometer.

Answer:

(a) - 3°C
(b) As the height increases, the temperature increases.
(c) $\frac{1}{6}$ °C per kilometer