Question

1. the table shows the admission costs (in dollars) and the average number of daily visitors at an amusement park each year for the past 8 years. find an equation of a line of fit. what is the expected daily attendance when admission is free?

cost (dollars), x 20 21 22 24 25 27 28 30
daily attendance, y 940 935 940 925 920 905 910 890

Explanation:

Step1: Calculate the slope (m)

First, we need two points to find the slope. Let's take the first two points \((20, 940)\) and \((30, 890)\).
The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\)
\(m=\frac{890 - 940}{30 - 20}=\frac{- 50}{10}=- 5\)

Step2: Find the y - intercept (b)

Using the point - slope form \(y - y_1=m(x - x_1)\) with the point \((20,940)\) and \(m=-5\)
\(y - 940=-5(x - 20)\)
\(y-940=-5x + 100\)
\(y=-5x+100 + 940\)
\(y=-5x + 1040\)

Step3: Find the attendance when admission is free (x = 0)

Substitute \(x = 0\) into the equation \(y=-5x + 1040\)
\(y=-5(0)+1040=1040\)

Answer:

The equation of the line of fit is \(y=-5x + 1040\) and the expected daily attendance when admission is free is \(1040\)