This data was taken from an unbiased study of beach chair rentals. Determine if the statements below are true or false.
Beach chair rentals go up $100 for every 3 degrees higher in temperature
The equation for the line that best fits this data is y = 100/3x + 100
If the temperature is around 28 degrees, then you could make about $900 in beach chair rentals
To determine the truth of the statements, we need to analyze the information provided and perform some calculations based on the given linear equation. Let's look at each statement in turn.
Statement 1: Beach chair rentals go up $100 for every 3 degrees higher in temperature.
To evaluate this statement, let's examine the slope of the given equation for the line of best fit. The equation provided is:
y = (100/3)x + 100
The slope of the line is the coefficient of x, which is (100/3). The slope tells us how much y changes for a one-unit change in x. Since we're dealing with temperatures and rental prices, it means that for every 3-degree increase in temperature (x), the beach chair rentals (y) theoretically increase by $100. Therefore:
Slope = Δy / Δx = $100 / 3 degrees
Statement 1 is true based on the given equation.
Statement 2: The equation for the line that best fits this data is y = 100/3x + 100.
We were provided with this equation and told it's the line that best fits the data from an unbiased study. Without additional data or evidence to dispute this claim, we would accept it as given. However, it is not possible to verify the accuracy of this statement without the actual study or data. For the sake of this question, we will assume this statement is true as provided.
Statement 3: If the temperature is around 28 degrees, then you could make about $900 in beach chair rentals.
To check this statement, we can use the given equation to find the predicted rental revenue when the temperature is 28 degrees.
y = (100/3)x + 100
Plug x = 28 into the equation:
y = (100/3)(28) + 100
y = (2800/3) + 100
y = 933.33 + 100
y = 1033.33
The prediction for a 28-degree temperature is approximately $1033.33, not $900. Therefore, statement 3 is false based on the provided equation.