A helicopter decends until it reaches the ground. The equation y= -300x + 1200 gives the height, y, in feet, x minutes after the pilot begins the descent. Graph the equation

Answer 1

To graph the equation \( y = -300x + 1200 \), we can start by identifying key components such as the y-intercept and the slope.

1. Y-Intercept: This occurs when \( x = 0 \): \[ y = -300(0) + 1200 = 1200 \] So, the y-intercept is \( (0, 1200) \). This means the helicopter starts at a height of 1200 feet.

2. Slope: The slope of the equation is -300. This indicates that for every minute (1 unit increase in \( x \)), the height \( y \) decreases by 300 feet.

3. Determine another point: To find another point, we can select a value for \( x \). Let's use \( x = 4 \): \[ y = -300(4) + 1200 = -1200 + 1200 = 0 \] So, when \( x = 4 \), the height \( y = 0 \) feet, which indicates that the helicopter reaches the ground after 4 minutes.

Points for the graph:

• Point 1: \( (0, 1200) \) - Starting point at 1200 feet.
• Point 2: \( (4, 0) \) - Ground level after 4 minutes.

Plotting the points:

1. Start by plotting the point \( (0, 1200) \) on the y-axis.
2. Next, plot the point \( (4, 0) \) on the x-axis.

Drawing the line:

Connect these two points with a straight line, which will slope downwards to the right, reflecting the negative slope of the equation.

Summary of the graph:

• The line starts at \( (0, 1200) \) and goes down to \( (4, 0) \).
• The entire line represents the descent of the helicopter, showing that as time increases, the height decreases linearly until it reaches the ground.

You can use graphing software or graph paper to create a more accurate visualization, using the slope and points identified above to help with the graphing.

Answer 2

Graph the equation y = 2

Answer 3

The equation \( y = 2 \) represents a horizontal line in the Cartesian coordinate system. Here’s how to graph this equation step-by-step:

Step 1: Understand the Equation

• The equation \( y = 2 \) means that no matter what value \( x \) takes, \( y \) will always be 2.

Step 2: Identify Key Points

You can choose any values for \( x \) to find corresponding points:

• When \( x = -2 \): \( y = 2 \) → Point: \( (-2, 2) \)
• When \( x = 0 \): \( y = 2 \) → Point: \( (0, 2) \)
• When \( x = 3 \): \( y = 2 \) → Point: \( (3, 2) \)

Step 3: Plot the Points

On a coordinate grid:

• Plot the points \( (-2, 2) \), \( (0, 2) \), and \( (3, 2) \).

Step 4: Draw the Line

• Connect the points with a straight horizontal line that extends infinitely in both the left and the right direction, keeping the line at \( y = 2 \).

Summary

The graph of the equation \( y = 2 \) will be a straight, horizontal line that crosses the y-axis at \( 2 \). This line does not rise or fall; it remains constant at \( y = 2 \) for all values of \( x \).

You can reference the x-axis and the y-axis to see how the line appears at that height. If you were to graph it digitally or on graph paper, it would look as a continuous line parallel to the x-axis, exactly two units above it.