Question

The graph relates the temperature change y (in degrees Fahrenheit) to the altitude change a (in thousands of feet).

Altitude Change
0 1 2 3 4 5 6 7 8 9 10
0
x
-5
-10
-15
-20
Temperature (°F)
-25
-30
-35
yy
Altitude (thousands of feet)
a. Choose the statement that best explains why the relationship is or is not proportional.
The relationship is proportional because the line passes through the origin.
O The relationship is proportional because the line has a negative slope.
O The relationship is not proportional because the line passes through the origin.
O The relationship is not proportional because the line has a negative slope.

Answer 1

The temperature change in relation to altitude change is proportional if the graph is a straight line passing through the origin and has a constant negative slope, indicating a consistent decrease in temperature with increased altitude.

Step-by-step explanation:

The relationship between temperature change and altitude change is described as proportional if it satisfies two conditions: the graph of the relationship is a straight line and it passes through the origin (0,0). Given the graph that relates temperature change (y) to altitude change (a), if the temperature decreases by a consistent amount for every thousand feet of altitude gained (i.e., the line has a constant negative slope), and this line starts at the origin, then the relationship is proportional. In the context of the altitude-temperature relationship, a negative slope indicates that as altitude increases (the value along the horizontal axis), the temperature (along the vertical axis) decreases consistently. A proportional relationship with a negative slope indeed means that for every increase in one unit of x, there is a constant decrease in y. Considering this explanation, the correct statement is: 'The relationship is proportional because the line passes through the origin.'