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) at what height above the planets surface is the temperature 0°c? 5 kilometers (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. at what rate is the temperature decreasing? -8 °c per kilometer as the height increases, the temperature increases. at what rate is the temperature increasing? °c per kilometer

Explanation:

Step1: Find temperature - height relationship

From the graph, as height increases from 0 km to 5 km, temperature decreases from 40°C to 0°C.

Step2: Calculate rate of temperature change

The rate of change of a linear - relationship $y = mx + b$ (where $y$ is temperature and $x$ is height) is given by the slope $m=\frac{\Delta y}{\Delta x}$. Here, $\Delta y=0 - 40=- 40$°C and $\Delta x = 5-0 = 5$ km. So, $m=\frac{-40}{5}=-8$ °C per km.

Answer:

(a) 5 kilometers
(b) As the height increases, the temperature decreases. -8 °C per kilometer