Final answer:
The function representing the relationship between the distance the laser travels, in centimeters, as a function of the number of bounces can be written in point-slope form as y - y₁ = m(x - x₁), where (x₁, y₁) denotes the initial point and m represents the slope.
Step-by-step explanation:
When a laser beam bounces off surfaces, the distance it travels is determined by the number of bounces. Each bounce can be seen as a reflection, resulting in the laser traveling an increased distance. The point-slope form y - y₁ = m(x - x₁) represents a linear function where x denotes the number of bounces, and y represents the distance traveled by the laser. The slope, 'm', signifies the rate of change of distance concerning the number of bounces, capturing how much the distance increases with each bounce.
The initial point (x₁, y₁) refers to the starting position of the laser beam, typically at zero bounces, where the distance might be the initial value before any bounces occur. By calculating the slope from the data or by establishing a pattern based on the number of bounces and corresponding distances traveled, we can determine the value of 'm' and plug it into the point-slope form to represent this relationship mathematically.
This point-slope equation provides a clear representation of the linear relationship between the number of bounces and the distance traveled by the laser beam, allowing for predictions of distance as the number of bounces increases.