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) what is the temperature at 0 kilometers?
(square) °c
(b) choose the statement that best describes how the height and temperature are related. then fill in the blank.
(\bigcirc) as the height increases, the temperature decreases.
at what rate is the temperature decreasing?
(square) °c per kilometer
(\bigcirc) as the height increases, the temperature increases.
at what rate is the temperature increasing?
(square) °c per kilometer

Explanation:

Step1: Find temp at 0 km

From the graph, at height $x=0$ km, the temperature $y=40^\circ\text{C}$.

Step2: Identify relationship trend

Observe the graph: as height increases, temperature falls. So select "As the height increases, the temperature decreases."

Step3: Calculate rate of change

Use two points: $(0, 40)$ and $(5, 4)$. Rate = $\frac{\text{Change in Temp}}{\text{Change in Height}} = \frac{4 - 40}{5 - 0} = \frac{-36}{5} = -7.2$. The negative sign means decreasing at $7.2^\circ\text{C}$ per kilometer.

Answer:

(a) $40$
(b)

• Selected statement: As the height increases, the temperature decreases.
• Rate of temperature decrease: $7.2$ °C per kilometer