To graph the equation \(y = 300x + 1200\), we first need to understand its components:
- y represents the height in feet.
- x represents the time in minutes after the pilot reaches the desert.
- The equation shows a linear relationship between height and time, where the intercept and slope can be interpreted as follows:
- The y-intercept, \(1200\), represents the height in feet when \(x = 0\) (the starting height).
- The slope, \(300\), indicates that the helicopter's height decreases by 300 feet for every minute that passes.
Steps to Graph the Equation:
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Determine the Y-Intercept:
- When \(x = 0\): \[ y = 300(0) + 1200 = 1200 \]
- Plot the point (0, 1200).
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Determine Another Point:
- Choose a value for \(x\). Let's say \(x = 2\): \[ y = 300(2) + 1200 = 600 + 1200 = 1500 \]
- Plot the point (2, 1500).
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Linear Trend:
- Since the equation is linear, draw a straight line through these points.
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Determine Additional Points for Accuracy:
- To ensure accuracy, find another point:
- Choose \(x = 4\): \[ y = 300(4) + 1200 = 1200 + 1200 = 2400 \]
- Plot the point (4, 2400).
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Draw the Line:
- Connect these points with a straight line and extend it as necessary in both directions.
Graph Features:
- The line will slope upwards because the coefficient of \(x\) is positive, which indicates an increase in height over time.
- Although the problem mentions descending, the equation indicates increasing height. If you want to show descending, the initial condition or equation might need to be inverted or adjusted.
Important Values:
- Starting height: 1200 feet when \(x = 0\).
- The height increases by 300 feet each minute.
Final Note:
Make sure to label the axes appropriately and indicate the units (feet for height and minutes for time). Since this is a helicopter scenario, you might want to include labels regarding its descent or flight. Typically, if it descends, you'd expect a negative slope or negative output for height as time progresses, which is contrary to this equation. If the scenario is to represent descent, we would need an equation of the form \(y = -300x + 1200\).
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