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

Explanation:

Step1: Analyze the graph for part (a)

The graph shows temperature (y - axis) vs height (x - axis). We need to find the height when temperature is \(0^\circ C\). From the graph, we can see the points: when height \(x = 5\) km, temperature \(y=0^\circ C\)? Wait, no, let's check the axes. Wait, the y - axis is temperature (\(^\circ C\)) and x - axis is height (km). Wait, the line goes from (0, 40) to (5, 0)? Wait, no, the x - axis is height (kilometers) and y - axis is temperature. So when temperature \(y = 0^\circ C\), what is \(x\) (height)? Looking at the graph, the line connects (0, 40) (when height is 0, temperature is \(40^\circ C\)) and (5, 0) (when height is 5 km, temperature is \(0^\circ C\))? Wait, no, the x - axis is height (kilometers) with labels 0,1,2,3,4,5,... and y - axis is temperature with labels 0,4,8,12,16,20,24,28,32,36,40. So the two points on the line are (0, 40) and (5, 0). So for part (a), when temperature is \(0^\circ C\), height is 5 kilometers.

Step2: Analyze the relationship for part (b)

The slope of the line will tell us the rate. The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using points (0, 40) and (5, 0), \(m=\frac{0 - 40}{5 - 0}=\frac{- 40}{5}=- 8\). So as height (x) increases, temperature (y) decreases. The rate is \(8^\circ C\) per kilometer decrease (since slope is - 8, meaning for each kilometer increase in height, temperature decreases by \(8^\circ C\)).

Answer:

(a) 5 kilometers
(b) As the height increases, the temperature decreases. The rate is \(8^\circ C\) per kilometer.