Question

Sketch a graph to envision the following scenario. Place time on the x-axis. A rock climber is 25 feet above sea level. After 8 seconds he is at sea level. (He did not fall). What is the slope of the line depicted (no units)

Answer 1

Please refer to the attached graph.

Slope = -3.125

Explanation:

Given

Time is placed on x axis.

Initially, height of rock climber is 25 feet above sea level.

`t_1 =0\ sec`

`h_1` = 25 feet

After 8 seconds, he is at sea level.

`t_2 =8\ sec`

`h_2` = 0 feet

To find:

Graph of the given points and Slope of the line depicted.

Solution:

Kindly refer to the attached graph.

Here, we have been given two points to be plotted on the xy coordinate plane.

1st point is (0, 25): Time is 0 and height above sea level is 25 ft

2nd point is (8, 0): Time is 8 seconds and height above sea level is 0 ft (i.e. he comes to sea level)

First of all, mark these points and join them with a straight line.

Please refer to attached graph.

Slope of a line is given as:

`m=(y_2-y_1)/(x_2-x_1)`

Here,

`y_2 = 0\\y_1 = 25\\x_2 = 8\\x_1 = 0`

Using the formula:

`m=(0-25)/(8-0)\\\Rightarrow m=-(25)/(8) = \bold{-3.125}`