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S-ID.3.7
A scatterplot is made of a city's population over time. The equation of the line of best fit is p =
629t + 150,000 where p is the city's predicted population size and t is the number of years since
2000. What is the meaning of the slope of this line?
A. In 2000, the city's population was about 629 people.
B. In 2000, the city's population was about 150,000 people.
C. The city's population increases by about 629 people each year.
D. The city's population increases by about 150,000 people each year.



Answer :

GinnyAnswer
The equation of the line of best fit is given by: \[ p = 629t + 150,000 \] where \( p \) represents the predicted population size of the city and \( t \) is the number of years since 2000. In a linear equation of the form: \[ y = mx + b \] - \( m \) represents the slope of the line - \( b \) represents the y-intercept of the line Relating this to the given equation: - The slope (\( m \)) is 629 - The y-intercept (\( b \)) is 150,000 The slope of a line in a graph depicting a change over time typically indicates the rate of change. Therefore, in the context of the given equation, the slope (629) represents the rate at which the city's population is changing with respect to each year since 2000. Hence, the meaning of the slope 629 in this line is that the city's population increases by about 629 people each year. So the correct answer to the question is: \[ \text{(C) The city's population increases by about 629 people each year.} \]

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