Suppose Zoe worked overtime at her job during a recent pay period, which is considered beyond 40 hours. Let the function P(t)=36t+960 represent the gross pay in dollars for Zoe as a function of the number of overtime hours worked, t
. What do the slope and y
-intercept of P(t) represent in this situation? Select the two correct answers.(1 point)
Responses
The slope represents Zoe earning $36 for each hour of overtime.
The slope represents Zoe earning $36 for each hour of overtime.
The y
-intercept represents Zoe has a gross pay of $36 when she works 0 hours for the pay period.
The y-intercept represents Zoe has a gross pay of $36 when she works 0 hours for the pay period.
The y
-intercept represents Zoe has $960 of gross pay when she works 0 hours for the pay period.
The y-intercept represents Zoe has $960 of gross pay when she works 0 hours for the pay period.
The slope represents Zoe earning $36 for each hour worked in the first 40 hours of the pay period.
The slope represents Zoe earning $36 for each hour worked in the first 40 hours of the pay period.
The y
-intercept represents Zoe has $960 of gross pay when she works a total of exactly 40 hours for the pay period.
The y-intercept represents Zoe has $960 of gross pay when she works a total of exactly 40 hours for the pay period.
The correct answers are:
1) The slope represents Zoe earning $36 for each hour of overtime.
2) The y-intercept represents Zoe has $960 of gross pay when she works 0 hours for the pay period.
The correct answers are:
1. The slope represents Zoe earning $36 for each hour of overtime.
2. The y-intercept represents Zoe has $960 of gross pay when she works 0 hours for the pay period.
The correct answers are:
1. The slope represents Zoe earning $36 for each hour of overtime.
2. The y-intercept represents Zoe has $960 of gross pay when she works 0 hours for the pay period.
To understand why these answers are correct, let's break down the function P(t) = 36t + 960:
1. The slope of the function is 36. In this context, it means that for each hour of overtime worked (represented by t), Zoe earns $36. So, for every additional hour she works beyond the regular 40 hours, her pay increases by $36.
2. The y-intercept of the function is 960. When t (the number of overtime hours worked) is 0, this means Zoe has not worked any overtime. In other words, her total working hours for the pay period are limited to the regular 40 hours. At this point, her gross pay is $960, which represents her base salary for working the regular hours without any overtime.
Therefore, the slope represents Zoe's additional earnings per hour of overtime worked, and the y-intercept represents Zoe's base pay when she does not work any overtime.