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Karen cleans office buildings. The graph shows the linear relationship between the time she spent cleaning and the number of offices cleaned. What is the rate of change of the number of offices cleaned with respect to the time she has spent cleaning? HOURS SPENT CLEANING

Karen cleans office buildings. The graph shows the linear relationship between the time she spent cleaning and the number of offices cleaned. What is the rate of change of the number of offices cleaned with respect to the time she has spent cleaning? \newlineHOURS SPENT CLEANING\text{HOURS SPENT CLEANING}

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Q. Karen cleans office buildings. The graph shows the linear relationship between the time she spent cleaning and the number of offices cleaned. What is the rate of change of the number of offices cleaned with respect to the time she has spent cleaning? \newlineHOURS SPENT CLEANING\text{HOURS SPENT CLEANING}
  1. Identify Points: Identify the points on the graph to calculate the rate of change. Suppose the graph shows that Karen cleaned 44 offices in 22 hours and 1010 offices in 55 hours.
  2. Calculate Rate of Change: Calculate the rate of change using the formula (change in y)/(change in x)(\text{change in } y) / (\text{change in } x). Here, change in y=number of offices cleaned\text{change in } y = \text{number of offices cleaned}, and change in x=hours spent cleaning\text{change in } x = \text{hours spent cleaning}. So, (10−4)/(5−2)=6/3(10 - 4) / (5 - 2) = 6 / 3.
  3. Simplify Fraction: Simplify the fraction to find the rate of change. 6/3=26 / 3 = 2. This means Karen cleans 22 offices per hour.

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