Writing a Linear Model:

Mathematical model – is a formula or equation that represents a relationship between two or more variables in a real-world application

Examples:

1.) Buffalo, New York, had 2 ft (24 in.) of snow on the ground before a snowstorm. During the storm, snow fell at an average rate of in./hr.

a.) Write a linear equation to compute the total snow depth y after x hr of the storm.

b.) Graph the equation.

c.) Use the equation to compute the depth of snow after 8 hr.

d.) If the snow depth was 31.5 in. at the end of the storm, determine how long the storm lasted.

Interpreting a Linear Model:

Example:

1.) In , President Franklin D. Roosevelt signed a bill enacting the Fair Labor Standards Act of (FLSA). In its final form, the act banned oppressive child labor and set the minimum hourly wage cents and the maximum workweek at hr. Over the years, the minimum hourly wage has been increased by the government to meet the rising cost of living.

The minimum hourly wage y (in dollars per hour) in the United States since can be approximated by the equation, where x represents the number of years since ( corresponds to , corresponds to , and so on).

a.) Determine the slope of the line and interpret the meaning of the slope as a rate of change.

b.) Find the -intercept of the line and interpret the meaning of the -intercept in the context of this problem.

c.) The year is years after the year . Substitute into the linear equation and find the minimum wage for . The actual minimum wage in was . What do you think is a possible reason for the difference?

d.) According to the linear model what should the minimum wage be today? . (current minimum wage in upstate NY is ; will increase to on December 31, 2017)

Explain the reason for any discrepancy

Writing a Linear Model from Observed Data Points:

Example:

1.) The figure below represents the number of women, y (in thousands), who graduated from law school in the United States by year. Let x represent the number of years since

a.) Use the given ordered pairs to find a linear equation to model the number of women graduating from law school by year.

b.) Determine the slope of the line and interpret the meaning of the slope as a rate of change.

c.) Use the linear equation to predict the number of women who will graduate from law school in the year .

d.) Would it be practical to use the linear model to predict the number of women who would graduate from law school for the year ? Explain your answer.

Practice:

One cell-phone plan charges a monthly fee plus a charge per minute for the number of minutes used beyond minutes. If a customer exceeds the minute cap, then the monthly fee y (in dollars), is given by, where x is the number of minutes used beyond minutes.

a.)What is the slope? Interpret its meaning in the context of the problem.

b.)What is the -intercept? Interpret its meaning in the context of the problem.

c.)Use the equation to determine the cost of using min in this plan.

2-4 CLASSWORK: pg. 176-178 #10, 13, 14, 15

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