GED Mathematical Reasoning TestAlgebraic Problem Solving with Graphs and FunctionsMedium
A meteorologist is tracking a weather balloon. The altitude of the balloon, in meters, is given by the equation A = 20t + 500, where t is the time in minutes. Which of the following statements about the balloon's movement is true?
- AThe balloon starts at an altitude of 20 meters.
- BThe balloon rises at a rate of 500 meters per minute.
- CThe balloon's altitude increases by 20 meters every minute.
- DThe balloon will reach 520 meters in 20 minutes.
Show answer & explanationAnswer & explanation
Correct answer: C. The balloon's altitude increases by 20 meters every minute.
In the linear equation A = 20t + 500, the coefficient of 't' (which is 20) represents the slope. The slope indicates the rate of change of the altitude with respect to time. Therefore, the balloon's altitude increases by 20 meters every minute. The constant term, 500, is the y-intercept, representing the initial altitude at t=0.
Why the other options are wrong
- A. The starting altitude (at t=0) is 500 meters (the y-intercept).
- B. The rate of rise is 20 meters per minute (the slope), not 500.
- D. To reach 520 meters, 20t + 500 = 520 => 20t = 20 => t = 1 minute, not 20 minutes.
Interpreting Linear Equations
A linear equation in the form y = mx + b represents a straight line. 'm' is the slope, indicating the rate of change, and 'b' is the y-intercept, indicating the initial value or starting point.
- Slope (m) describes how much y changes for each unit change in x.
- Y-intercept (b) is the value of y when x is 0.
- Contextual meaning is crucial: slope is often a rate, y-intercept is an initial amount.
Memory trick: Y = mx + b tells all!