Question

lesson 4: linear models
cool down: roar of the crowd
the scatter plot shows the maximum noise level when different
numbers of people are in a stadium. the linear model is given by the
equation ( y = 1.5x + 22.7 ), where ( y ) represents maximum noise level
and ( x ) represents the number of people, in thousands, in the stadium.
( y = 1.5x + 22.7 )

1. the slope of the linear model is 1.5. what does this mean in

terms of the maximum noise level and the number of people?

Explanation:

Step1: Recall the slope - intercept form of a linear equation

The equation of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. In the given equation \(y = 1.5x+22.7\), \(y\) is the maximum noise level (in decibels) and \(x\) is the number of people (in thousands).

Step2: Interpret the slope

The slope \(m = 1.5=\frac{\Delta y}{\Delta x}\). The change in \(y\) (\(\Delta y\)) represents the change in the maximum noise level and the change in \(x\) (\(\Delta x\)) represents the change in the number of people (in thousands).

Answer:

For every additional 1 thousand people in the stadium, the maximum noise level increases by 1.5 decibels.