Question

baseball for exercises 5 - 7, use the scatter plot that shows the average price of a major - league baseball ticket from 1991 to 2005.

1. determine what relationship, if any, exists in the data. explain.
2. use the points (1998, 13.60) and (2003, 19.00) to write the slope - intercept form of an equation for the line of fit shown in the scatter plot.
3. predict the price of a ticket in 2009.

Explanation:

Question 5

A positive linear relationship exists. As the years (from 1991 - 2005) increase, the average price of a major - league baseball ticket also increases. The scatter plot shows points that generally follow an upward - sloping trend.

Step1: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(1998,13.60)\) and \((x_2,y_2)=(2003,19.00)\).

$$m=\frac{19.00 - 13.60}{2003 - 1998}=\frac{5.4}{5}=1.08$$

Step2: Use the point - slope form \(y - y_1=m(x - x_1)\) to find the \(y\) - intercept \(b\)

Using the point \((x_1,y_1)=(1998,13.60)\) and \(m = 1.08\), we have \(y-13.60=1.08(x - 1998)\).

$$y=1.08x-1.08\times1998 + 13.60$$

$$y=1.08x-2157.84+13.60$$

$$y=1.08x - 2144.24$$

Step1: Use the equation from question 6 (\(y = 1.08x-2144.24\))

Substitute \(x = 2009\) into the equation \(y=1.08x - 2144.24\)

$$y=1.08\times2009-2144.24$$

$$y = 2169.72-2144.24$$

$$y=25.48$$

Answer:

A positive linear relationship exists. As the years increase, the ticket price increases.

Question 6