Question

2. A skydiver jumps from a plane from an altitude of 8000 ft. An observer on the ground measures the skydiver’s altitude at time t = 0 to be 7500 ft. The linear graph shows the skydiver’s altitude at various times during her descent.

(a) Identify the y-intercept. How does the y-intercept relate to the skydiver’s position relative to the ground? Explain.
(b) Determine the slope of the line. According to the slope, is the skydiver ascending or descending and what is the rate of ascent or descent? Explain.
(c) Identify the x-intercept. What does the x-intercept mean in this context? Explain.
(d) Write an equation for the line.
Answer:

Answer 1

(a) The y-intercept of a linear graph is the point where the line crosses the y-axis. In this case, the y-intercept is (0, 7500), which means that at time t = 0, the skydiver was at an altitude of 7500 ft. The y-intercept therefore represents the skydiver's starting altitude relative to the ground.

(b) The slope of a line is a measure of the steepness of the line and is calculated using the formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are two points on the line.

To find the slope of the line, we can choose two points on the line and substitute their coordinates into the formula. For example, we could choose the points (0, 7500) and (30, 5000). Substituting these values into the formula, we find that the slope of the line is:

slope = (5000 - 7500) / (30 - 0)
= -2500 / 30
= -83.333

This means that the skydiver is descending at a rate of 83.333 ft/s.

(c) The x-intercept of a linear graph is the point where the line crosses the x-axis. In this case, the x-intercept is (60, 0), which means that at time t = 60, the skydiver's altitude was 0 ft. The x-intercept therefore represents