Question

1. the scatter plot shows the number of minutes (min.) people had to wait for service at a restaurant and the number of staff available at the time. 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. the slope of the line is -1.62. what does this mean in this situation? is it realistic?
b. the y - intercept is (0,18). what does this mean in this situation? is it realistic?

Explanation:

Step1: Interpret slope

The slope - 1.62 means that for every 1 - unit increase in the number of staff available ($x$), the wait - time ($y$) decreases by 1.62 minutes. This is realistic as more staff generally leads to faster service and shorter wait - times.

Step2: Interpret y - intercept

The y - intercept (0, 18) means that when there are 0 staff available, the wait - time is 18 minutes. This is somewhat realistic as even with no staff, there may still be some pre - existing processes or a backlog that causes a wait.

Answer:

a. The slope of - 1.62 means that for each additional staff member, the wait time decreases by 1.62 minutes. It is realistic.
b. The y - intercept (0, 18) means that when there are no staff members, the wait time is 18 minutes. It is somewhat realistic.