Question

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

From the graph, when the height is 0 kilometers, the temperature is read - 10°C.

Step2: Determine the relationship between height and temperature

The graph shows a positive - slope linear relationship. As the height increases, the temperature increases.

Step3: Calculate the rate of temperature change

Pick two points on the line, say (0, - 10) and (10, 10). The rate of change (slope $m$) is calculated using the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, where $x$ is height (in kilometers) and $y$ is temperature (in °C). So $m=\frac{10-(-10)}{10 - 0}=\frac{20}{10}=2$ °C per kilometer.

Answer:

(a) - 10°C
(b) As the height increases, the temperature increases.
2 °C per kilometer