Question

scientists are measuring a distant planet’s temperature. the graph shows the temperature (in °c) versus the height (in kilometers) above the planet’s surface.
(a) choose the statement that best describes how the height and temperature are related. then fill in the box.

• 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
(b) what is the temperature at 0 kilometers?
______°c

Explanation:

Step1: Identify two points on the line

From the graph, we can see two points: when height \( h = 0 \) km, temperature \( T = 20^\circ \text{C} \); when height \( h = 8 \) km, temperature \( T = 0^\circ \text{C} \).

Step2: Calculate the rate of change (slope)

The slope \( m \) of a line is given by \( m=\frac{\Delta T}{\Delta h}=\frac{T_2 - T_1}{h_2 - h_1} \). Substituting the values \( T_1 = 20 \), \( T_2 = 0 \), \( h_1 = 0 \), \( h_2 = 8 \), we get \( m=\frac{0 - 20}{8 - 0}=\frac{- 20}{8}=- 2.5 \). This means the temperature decreases by \( 2.5^\circ \text{C} \) per kilometer increase in height.

Step3: Find the temperature at 0 kilometers

From the graph, when \( h = 0 \) km, we can directly see (or from the y - intercept of the line) that the temperature \( T = 20^\circ \text{C} \).

Answer:

(a) The statement "As the height increases, the temperature decreases" is correct. The rate is \( - 2.5^\circ \text{C} \) per kilometer (or we can say the temperature decreases at a rate of \( 2.5^\circ \text{C} \) per kilometer).
(b) The temperature at 0 kilometers is \( 20^\circ \text{C} \)