Final answer:
The linear equation y = -10x + 3000 represents the height of the skydiver at any time, where -10 is the rate of descent and 3000 is initial height. The x-intercept of 300 indicates it would take the skydiver 300 seconds to reach the ground. The slope of -10 means the skydiver falls at a rate of 10 feet per second.
Step-by-step explanation:
The equation given for the height of the skydiver, y = -10x + 3000, is a linear equation representing a straight line.
Graphing the Equation
To graph this equation, we plot the y-intercept at (0, 3000) and use the slope to find other points. Since the slope is -10, for every 1 second that passes, the skydiver descends 10 feet. Plotting these points and drawing a straight line through them gives us the graph. The x-axis represents time in seconds, and the y-axis represents height in feet.
Interpreting the x-intercept
The x-intercept is the point where the graph crosses the x-axis. To find it, set y to 0 and solve for x: 0 = -10x + 3000, which simplifies to x = 300. This means the skydiver will reach the ground after 300 seconds.
Interpreting the Slope
The slope of the equation (-10) signifies the rate of descent; for each second, the skydiver falls 10 feet.
Meaning of x-intercept
The x-intercept represents the total time taken by the skydiver to reach the ground from 3000 feet.