Question

a construction worker is using a crane to lower a steel beam to the ground. there is a linear relationship between the time the beam is being lowered, in minutes, and the height of the beam, in feet. describe the rate of change for this relationship. the beams height by per minute.

Explanation:

Step1: Recall the formula for slope (rate of change)

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points from the graph. The \(y\) - axis represents height (in feet) and the \(x\) - axis represents time (in minutes). The line passes through the points \((0,180)\) and \((18,0)\).

Step2: Substitute the values into the slope formula

Here, \(x_1 = 0,y_1=180,x_2 = 18,y_2 = 0\). Then \(m=\frac{0 - 180}{18-0}\).

$$m=\frac{- 180}{18}=-10$$

Answer:

The beam's height decreases by \(10\) feet per minute.