The graph of the linear function shown models the altitude, in meters, of a hot-air balloon minutes after it begins to descend.
Which choice is the rate at which the balloon’s altitude is changing, in meters per minute?
When a linear graph represents a quantity over time, the rate of change is the slope. Pick two clear points on the line, compute , and use the sign (increasing vs. decreasing) to confirm the result.
Hints
Use rise over run
The rate of change of a linear graph is its slope: .
Watch the sign
If the altitude is decreasing as time increases, the slope (rate) should be negative.
Desmos Guide
Plot two points from the graph
In Desmos, enter the points and .
Compute the slope
Compute the slope using , then simplify to get the rate in meters per minute.
Step-by-step Explanation
Find the slope from two points
From the graph, the line passes through and . The slope is
Interpret the slope as the rate of change
Compute the slope:
So the balloon’s altitude is changing at meters per minute (choice ).