Question

The linear equation graphed above gives the height in feet above the ground of Shelly t seconds after she opened her parachute when jumping from an airplane. According to the graph, how many seconds after opening her parachute will Shelly be 2,000 feet above the ground?

Answer 1

Answer:

$\large \boxed{\text{60 s}}$

Step-by-step explanation:

Assume your graph looks like the one below.

1. Calculate the equation of the straight line

The slope-intercept equation for a straight line is

y = mx + b

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

The line passes through the points (0,2600) and (30, 2300)

(a) Calculate the slope of the line

$\begin{array}{rcl}m & = & \dfrac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\ & = & \dfrac{2300 - 2600}{30 - 0}\\\\& = & \dfrac{-300}{30}\\\\& = & \text{-10 ft/s}\\\\\end{array}$

(b) Locate the y-intercept

The y-intercept is at 2600 ft

(c) Write the equation for the line

h = -10t + 2600

(d) Calculate the time to 2000 ft

$\begin{array}{rcl}h & = & -10t + 2600\\2000 & = & -10t + 2600\\-600 & = & -10t\\t & = & \dfrac{-600}{-10}\\\\& = & \text{60 s}\\\end{array}$

Shelley will be at 2000 ft 60 s after opening the parachute.