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) 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 the temperature at 0 kilometers

Looking at the graph, when the height (x - axis) is 0 kilometers, the corresponding temperature (y - axis) is \(5^{\circ}C\).

Step2: Determine the relationship between height and temperature

The graph is a straight - line (linear) graph. We can use the formula for the slope of a line \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0,5)\) and \((x_2,y_2)=(40,1)\).

$$m=\frac{1 - 5}{40-0}=\frac{- 4}{40}=-0.1$$

The negative slope means that as the height (\(x\)) increases, the temperature (\(y\)) decreases.

Step3: Find the rate of change

The rate of change (slope) of the line is \(-0.1^{\circ}C\) per kilometer. When we consider the rate at which the temperature is increasing (we take the absolute value of the slope for the rate of change in magnitude). But for the rate at which temperature is decreasing, it is \(0.1^{\circ}C\) per kilometer.

Answer:

(a) \(5^{\circ}C\)
(b) As the height increases, the temperature decreases at a rate of \(0.1^{\circ}C\) per kilometer.