Linear models

Scenario You have been offered three swim instructor positions for the summer. “Swimmers Unlimited” will pay you a flat salary of $100 every week. “Dive for It” will pay you $50 a week plus $1.50 for person that enrolls in the swim class. “Jump-In” will pay you $2.50 for each person that enrolls in the swim class. Based on the expected earnings, which job should you choose? -Allow students time to think, pair-share, and then share with the class. -Record the responses on chart paper. -Share with students that linear models can be used to model each of these jobs to make

y=25x+2000 Writing a linear model If the rate of change is constant (slope), a linear model can be written. The initial amount is the y-intercept. Example: A computer salesperson earns a base salary of $2,000 plus a commission of $25 per computer that he sells. This is the initial amount. This is the constant rate of change. Have students take notes as you go through this presentation. y=25x+2000

Swimmers unlimited At Swimmers Unlimited, you will earn a salary of $100 per week as a swim instructor, regardless of how many people sign up for swim lessons. Write an equation for earnings (E) in terms of the number of people taking swim lessons (p). Explain to students that there is no rate of change here, so the equation will not have a “slope.” E=100

Complete the table. Plot the points in your table on the graph below Complete the table. Plot the points in your table on the graph below. Then graph the equation of the line that you wrote to represent the expected earnings for this job.

Dive for it At Dive for It, you will earn a weekly salary of $50 plus $1.50 for each person who signs up to take swim lessons. Write an equation for earnings (E) in terms of the number of people taking swim lessons (p). Before writing the equation, solicit student answers to the following questions: -Is there a constant rate of change? -What is the rate of change? -What is the initial amount? E=$50+$1.50P

Complete the table. Plot the points in your table on the graph below Complete the table. Plot the points in your table on the graph below. Then graph the equation of the line that you wrote to represent the expected earnings for this job. Guide students through this portion. Have them check their work with a partner.

Jump-in At Jump-In, you will earn $2.50 for each person that signs up to take swim lessons. Write an equation for earnings (E) in terms of the number of people taking swim lessons (p). -Independent Practice: Have students write the equation independently. -Walk around and assist those that need it. -When most of the students have finished, go over the answer whole class. -E=$2.50P

Complete the table. Plot the points in your table on the graph below Complete the table. Plot the points in your table on the graph below. Then graph the equation of the line that you wrote to represent the expected earnings for this job. -Independent Practice: Have students write the equation independently. -Walk around and assist those that need it. -When most of the students have finished, go over the answer whole class.

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