Question

The table shows the elevation above the ground of a hang glider as the pilot glides it to the landing area. Assume the relationship between the two quantities is linear.

Time (min), x Elevation (ft), y
2 765
4 555
6 345
8 135


Find and interpret the rate of change.



The rate of change is
, so the hang glider is descending
feet each minute of flight.



Find and interpret the initial value.
The initial value is
, so the hang glider was initially
feet above the landing area.

Answer 1

To find the rate of change (slope) of the linear relationship between time and elevation, we can use the formula:

slope = (change in y) / (change in x)

Let's choose the first and last data points to find the slope:

slope = (135 ft - 765 ft) / (8 min - 2 min) = -120 ft/min

The negative slope means that the hang glider is descending at a rate of 120 feet per minute.

To find the initial value (y-intercept) of the linear relationship, we can use the slope-intercept form of a linear equation:

y = mx + b

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

Let's use the first data point to solve for b:

765 = -120(2) + b

b = 1005

Therefore, the equation for the linear relationship between time and elevation is:

y = -120x + 1005

The initial value (y-intercept) is 1005 feet, which means that the hang glider was initially 1005 feet above the landing area.