2. A skydiver jumps from a plane from an altitude of 6000 ft. An observer on the ground measures the skydiver’s altitude at time t = 0 to be 4500 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.

a. The y-intercept of the linear graph is (0, 4500).

b. The rate of descent is 1500 ft per minute.

c. The x-intercept of the linear graph is (3, 0).

d. The equation for the line representing the skydiver's altitude during descent is y = 4500 - 1500x.

(a) The y-intercept of the linear graph is (0, 4500). In this context, the y-intercept represents the initial altitude of the skydiver when time [tex]\( t = 0 \)[/tex], which is 4500 ft above the ground. It indicates the starting point of the skydiver's descent relative to the ground.

(b) To determine the slope of the line, we use the formula for slope:

[tex]\[ \text{Slope} = \frac{\text{change in } y}{\text{change in } x} \][/tex]

From the given points, we see that:

- Change in y = 4500 - 0 = 4500 ft

- Change in x = 0 - 3 = -3 minutes

Substituting these values into the slope formula:

[tex]\[ \text{Slope} = \frac{4500}{-3} = -1500 \text{ ft/minute} \][/tex]

Since the slope is negative, it indicates that the skydiver is descending. The rate of descent is 1500 ft per minute.

(c) The x-intercept of the linear graph is (3, 0). In this context, the x-intercept represents the time it takes for the skydiver to reach the ground, which is 3 minutes after jumping from the plane. At the x-intercept, the altitude of the skydiver is 0 ft, indicating that the skydiver has landed on the ground.

(d) The equation for the line can be written using the slope-intercept form:

[tex]\[ y = mx + b \][/tex]

where m is the slope and b is the y-intercept.

From the given information:

- Slope m = -1500 ft/minute

- y-intercept b = 4500 ft

Substituting these values into the slope-intercept form:

y = -1500x + 4500

Therefore, the equation for the line representing the skydiver's altitude during descent is y = 4500 - 1500x.

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