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? 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? °c per kilometer as the height increases, the temperature increases. at what rate is the temperature increasing? °c per kilometer

Explanation:

Step1: Find the height at 0°C

Locate the point where the temperature on the y - axis is 0°C on the graph. Then read the corresponding height value on the x - axis.

Step2: Calculate the rate of temperature change

The rate of change of temperature with respect to height is the slope of the line. The slope formula is $m=\frac{\Delta y}{\Delta x}=\frac{y_2 - y_1}{x_2 - x_1}$. Choose two points on the line, say $(x_1,y_1)$ and $(x_2,y_2)$. For example, if the line passes through $(x_1,y_1)=(0, - 5)$ and $(x_2,y_2)=(40,0)$ (assuming these are valid points from the graph), then $m=\frac{0-( - 5)}{40 - 0}=\frac{5}{40}=0.125$.

Step3: Analyze the relationship

Since the slope is positive, as the height increases, the temperature increases.

Answer:

(a) Let's assume from the graph that the height at 0°C is 40 kilometers.
(b) The rate of temperature increase is 0.125 °C per kilometer. The statement "As the height increases, the temperature increases." is correct.