Question

in 2016, 3.76 million spectators attended car races worldwide. in 2019, worldwide car race attendance was 4.12 million.
a. assume that the relationship between time, x, and car race attendance, y, is linear and write an equation describing this relationship. use ordered pairs of the form (years past 2016, number of spectators in millions).
b. use this equation to predict the number of spectators in 2022.
a. the equation describing the relationship is □.
(type your answer in slope - intercept form. use integers or decimals for any numbers in the equation.)

Explanation:

Step1: Calculate the slope

Let \(x_1 = 2016 - 2016=0\), \(y_1 = 3.76\); \(x_2=2019 - 2016 = 3\), \(y_2 = 4.12\).
The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
\(m=\frac{4.12 - 3.76}{3-0}=\frac{0.36}{3}=0.12\).

Step2: Write the slope - intercept form

The slope - intercept form is \(y=mx + b\). Using the point \((x_1,y_1)=(0,3.76)\), we know that \(b = 3.76\) (since when \(x = 0\), \(y=b\)).
So the equation is \(y=0.12x+3.76\).

Step3: Predict for 2022

For 2022, \(x = 2022 - 2016=6\).
Substitute \(x = 6\) into \(y=0.12x + 3.76\).
\(y=0.12\times6+3.76\).
\(y = 0.72+3.76\).
\(y=4.48\).

Answer:

a. The equation is \(y = 0.12x+3.76\).
b. The number of spectators in 2022 is \(4.48\) million.