Question

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

Locate the point on the graph where height = 0 km. The corresponding temperature value on the y - axis is the answer for part (a).

Step2: Determine rate of change

The rate of change of temperature with respect to height is the slope of the line. For a linear graph \(y = mx + b\), the slope \(m=\frac{\Delta y}{\Delta x}\). Here, \(y\) is temperature and \(x\) is height. We pick two points \((x_1,y_1)\) and \((x_2,y_2)\) on the line and calculate \(\frac{y_2 - y_1}{x_2 - x_1}\) to find the rate for parts (b) and (c).

Answer:

(a) [Read the temperature value at height = 0 km from the graph] °C
(b) As the height increases, the temperature decreases. At what rate is the temperature decreasing? [Calculated slope value] °C per kilometer
(c) As the height increases, the temperature increases. At what rate is the temperature increasing? [Calculated slope value] °C per kilometer (Note: Based on the description in part (c) which seems to be contrary to the graph trend shown, if the graph shows decrease, this part's statement is incorrect in context but we follow the format for response. The correct trend from the graph should be decrease as in part (b))