scientists are measuring a distant planets temperature. the graph shows the temperature (in °c) versus the…

scientists are measuring a distant planets temperature. the graph shows the temperature (in °c) versus the height (in kilometers) above the planets surface. (a) 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 (b) at what height above the planets surface is the temperature 0°c? kilometers

scientists are measuring a distant planets temperature. the graph shows the temperature (in °c) versus the height (in kilometers) above the planets surface. (a) 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 (b) at what height above the planets surface is the temperature 0°c? kilometers

Answer

Explanation:

Step1: Identify two points on the line

Let's take two points $(0,32)$ and $(8,0)$ from the graph.

Step2: Calculate the slope (rate of change)

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1 = 0,y_1=32,x_2 = 8,y_2 = 0$. So $m=\frac{0 - 32}{8-0}=\frac{-32}{8}=- 4$. The rate at which the temperature is changing is $4^{\circ}C$ per kilometer (the negative sign indicates a decrease).

Step3: Find the height when temperature is 0

From the graph, when $y = 0$, we can see that $x = 8$.

Answer:

(a) As the height increases, the temperature decreases. $4$ (b) $8$