Question

scientists are measuring a distant planets temperature. the graph shows the temperature (in °c) versus the height (in km). (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. at what rate is the temperature decreasing? °c per kilometer as the height increases, the temperature increases. at what rate is the temperature increasing? °c per kilometer

Explanation:

Step1: Find temperature at 0 km

On the graph, when the height (x - axis) is 0 km, the corresponding temperature (y - axis) is 45°C.

Step2: Analyze the relationship

The graph shows a downward - sloping line, which means as the height increases, the temperature decreases.

Step3: Calculate the rate of change

The line passes through the points (0, 45) and (3, 0). The rate of change (slope) $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0 - 45}{3-0}=\frac{- 45}{3}=-15$. The rate at which the temperature is decreasing is 15°C per kilometer.

Answer:

(a) 45
(b) As the height increases, the temperature decreases. 15