Question

the graph shows the temperature (in °c) versus the height (in kilor
(a) what is the temperature at 0 kilometers?
-4 °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?
0.5 °c per kilometer

Explanation:

Step1: Analyze the graph for part (a)

The height of \(0\) kilometers is the starting - point (y - intercept) of the relationship. By looking at the graph (assuming standard coordinate - based interpretation where \(x = 0\) gives the initial value for \(y\)), we can directly read the temperature at \(0\) kilometers.

Step2: Analyze the rate of change for part (b) (if the correct statement is "As the height increases, the temperature decreases")

The rate of change of a linear relationship \(y=mx + b\) (where \(y\) is temperature and \(x\) is height) is given by the slope \(m=\frac{\Delta y}{\Delta x}\). If we assume two points \((x_1,y_1)\) and \((x_2,y_2)\) on the line. For example, if we take \(x_1 = 0\) and \(y_1=-4\), and assume another point (say \(x = 8\) and \(y=-8\) - values based on a typical linear - graph interpretation for a decreasing function). Then \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-8-(-4)}{8 - 0}=\frac{-4}{8}=-0.5\). The rate of decrease is the absolute value of the slope.

Answer:

(a) \(-4^{\circ}C\)
(b) If the correct statement is "As the height increases, the temperature decreases", the rate is \(0.5^{\circ}C\) per kilometer.