A student is measuring the length of an icicle, y, every hour, x. The icicle is currently 9 inches long and is melting at a rate of 0.6 inches per hour. Find and interpret the slope for this relationship.

Question

9; the length of the icicle when the student first measures it
−9; the length of the icicle when the student first measures it
0.6; for every additional hour, the length of the icicle increases by 0.6 inches
−0.6; for every additional hour, the length of the icicle decreases by 0.6 inches

Answer 1

In this scenario, we are looking at the relationship between the length of the icicle (\(y\)) and time in hours (\(x\)). The icicle starts at a length of 9 inches and melts at a rate of 0.6 inches per hour.

The slope in the context of this problem represents the rate of change of the length of the icicle over time. Because the icicle is melting, this rate of change is negative.

Thus, the correct interpretation of the slope is:

• −0.6; for every additional hour, the length of the icicle decreases by 0.6 inches.

So, the slope indicates that as time increases by one hour, the length of the icicle decreases by 0.6 inches.