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

Step2: Find the y - intercept (b)

We can use the point - slope form \(y - y_1=m(x - x_1)\). Let's use 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 expected 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 \(1040\).