Question

standing on a flat field, a surveyor turned on his handheld laser and angled its beam slightly upward. at a distance of 4 meters from the surveyor, the laser beam was 2 meters above the ground. at a distance of 25 meters, the laser beam was 4.1 meters above the ground. complete the equation that describes the linear relationship between the height of the laser beam in meters, h, and the distance from the surveyor in meters, d. write your answer using whole numbers or decimals rounded to the nearest tenth. h = □d + □

Explanation:

Step1: Calculate the slope \(m\)

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(4,2)\) and \((x_2,y_2)=(25,4.1)\).

$$m=\frac{4.1 - 2}{25 - 4}=\frac{2.1}{21}=0.1$$

Step2: Find the \(y -\)intercept \(b\)

Use the point - slope form \(y - y_1=m(x - x_1)\). Substitute \(m = 0.1\), \(x_1 = 4\), and \(y_1=2\).

$$y-2=0.1(x - 4)$$

$$y-2=0.1x-0.4$$

$$y=0.1x + 1.6$$

Answer:

\(H = 0.1d+1.6\)