Question

a line that models the data is given by the equation ( y = -1.62x + 18 ), where ( y ) represents the wait time, and ( x ) represents the number of staff available.
a) what is the predicted wait time when there are 9 people on staff?
b) what is the slope? what does it mean in this situation?

Explanation:

Step1: Substitute \(x = 9\) into the equation

Given the equation \(y=-1.62x + 18\), substitute \(x = 9\)

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Step2: Calculate the value of \(y\)

$$ y=3.42 $$

Step3: Identify the slope

The equation of a line is \(y = mx + b\), where \(m\) is the slope. For the equation \(y=-1.62x + 18\), the slope \(m=-1.62\)

Step4: Interpret the slope

In the context of \(y\) (wait - time) and \(x\) (number of staff), the slope \(-1.62\) means that for each additional staff member (\(x\) increases by 1), the wait - time (\(y\)) decreases by \(1.62\) units.

Answer:

A) The predicted wait time when there are 9 people on staff is \(3.42\)
B) The slope is \(-1.62\). It means that for each additional staff member, the wait time decreases by \(1.62\) units.