Final Answer:
The linear equation in slope-intercept form that best models the situation is ( h(t) = -1.5t + 5 ), where ( h ) represents the height of the paper airplane above the ground (in feet) and ( t ) represents the time elapsed (in seconds).
Step-by-step explanation:
The equation ( h(t) = -1.5t + 5 ) is derived from the given information about the paper airplane's motion. The slope of the equation, -1.5, represents the rate at which the plane is descending per second. Since the plane starts at a height of 5 feet, the ( +5 ) in the equation accounts for the initial height.
In the context of this scenario, the equation captures the linear relationship between time and height as the paper airplane descends. The negative slope indicates a decrease in height over time, reflecting the downward motion of the airplane. The initial height of 5 feet is represented by the ( +5 ) constant term.
To illustrate, let's consider the scenario when ( t = 0 ) (the initial time). Substituting ( t = 0 ) into the equation gives ( h(0) = -1.5(0) + 5 = 5 ), confirming that the initial height is indeed 5 feet. Additionally, the negative coefficient of ( t ) signifies the constant rate of descent, 1.5 feet per second. This linear equation serves as a concise and accurate representation of the paper airplane's height as it travels across the room.