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?

Solution available with step-by-step explanation

SAT Linear Functions Question 34 | Free SAT Prep | Aniko

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Question 34·Easy·Linear Functions

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The graph of the linear function $A$ shown models the altitude, in meters, of a hot-air balloon $t$ 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 $\Delta y/\Delta x$ , and use the sign (increasing vs. decreasing) to confirm the result.

Hints

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Use rise over run

The rate of change of a linear graph is its slope: $\frac{\text{change in }y}{\text{change in }x}$ .

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 $(1,110)$ and $(6,60)$ .

Compute the slope

Compute the slope using $m=\frac{y_2-y_1}{x_2-x_1}=\frac{60-110}{6-1}$ , 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 $(1,110)$ and $(6,60)$ . The slope is

\frac{60-110}{6-1}.

Interpret the slope as the rate of change

Compute the slope:

\frac{-50}{5}=-10.

So the balloon’s altitude is changing at $-10$ meters per minute (choice $-10$ ).

Strategy

Hints

Desmos Guide

Step-by-step Explanation

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Strategy

Hints

Desmos Guide

Step-by-step Explanation