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Writing and Solving Linear Functions

This lesson aims to help students understand and apply linear functions to model and solve real-life scenarios. Students will learn to write equations based on problem descriptions and develop their skills in solving for a variable. Through practical examples, such as calculating hours worked by a window cleaner and managing savings for an MP3 player, students will grasp the significance of the constant and variable in linear equations. By the end of the lesson, learners will be equipped to tackle various problems using linear functions confidently.

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Writing and Solving Linear Functions

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  1. Writing and Solving Linear Functions

  2. Writing and Solving Linear Functions • Lesson Objective: NCSCOS 4.01 Use linear functions to model and solve problems; justify results. • Students will know how to write an equation from a problem. • Students will know how to solve equations for a variable.

  3. Writing and Solving Linear Functions • Tamara charges $25 per hour to clean windows. She also receives $5 for transportation to the job. One Saturday, Tamara earned $130. • The first step to solving a problem like this is to find the question. • What is the question asking for? • If we don’t know something what do we call it? How many hours did x Tamara work?

  4. Writing and Solving Linear Functions • Tamara charges to clean windows. She also receives $5 for transportation to the job. One Saturday, Tamara earned $130. How many hours did Tamara work? • We know that hours = • What goes with hours in the problem? • $25 $25 per hour x

  5. Writing and Solving Linear Functions • Start with the equation of a line: • We know that $25 goes with the x, so plug it in for m. • We now have to replace the “b” to get our equation y 25 = m x + b

  6. Writing and Solving Linear Functions • Tamara charges $25 per hour to clean windows. She also receives for transportation to the job. One Saturday, Tamara earned $130. How many hours did Tamara work? • “b” is the y-intercept or the constant so it doesn’t change • How much does Tamara make no matter how long she works? $5

  7. Writing and Solving Linear Functions • Replace the “b” with $5: • always represents a total. If there is a total in the problem, we will replace the y with the total 5 y = 25x + b y

  8. Writing and Solving Linear Functions • Tamara charges $25 per hour to clean windows. She also receives $5 for transportation to the job. One Saturday, How many hours did Tamara work? • Is there a total? • Therefore, y = $130 Tamara earned $130.

  9. Writing and Solving Linear Functions • Replace y with $130 • Solve for x: subtract 5 from both sides • Divide both sides by 25 130 125 y 5 = 25 x +5 - 5-5 25 25

  10. Writing and Solving Linear Functions You Try! • An MP3 player costs $195 including tax. You already have $37 and can save $9 per week. After how many weeks can you buy the player?

  11. Writing and Solving Linear Functions • An MP3 player costs $195 including tax. You already have $37 and can save per week. After how many can you buy the player? • Write the equation of a line • What is the question asking for? • x = # of weeks • What goes with the # of weeks? $9 weeks y = m x +b

  12. Writing and Solving Linear Functions • An MP3 player costs $195 including tax. You already have $37 and can save $9 per week. After how many can you buy the player? • Replace m with $9 • $37 doesn’t change since you already have that in the bank. Replace b with $37 • $195 is the total, so replace y with $195 weeks 195 y 9 = m x +b +37

  13. Writing and Solving Linear Functions 17.56 195 158 9 18 weeks = x +37 • Subtract 37 from both sides • Divide both sides by 9 • If the number of weeks isn’t an even number, round up -37-37 9 9

  14. Writing and Solving Linear Functions • An MP3 player costs $195 including tax. You already have $37 and can save $9 per week. After how many weeks can you buy the player? • In 18 weeks you will have enough for the Mp3 player

  15. Writing and Solving Linear Functions • A telephone calling card allows 25¢ per minute plus a one-time service charge of 75¢. How many minutes can Rob talk if he paid $5 for the card? Try Again!

  16. Writing and Solving Linear Functions • The Brown’s computer repair bill was $225. This included $75 for parts and $50 for each hour of labor. How many hours did the computer repairman work? • A local airport charges $12 for the first day of parking and $9 for each additional day. Gus paid $120 for parking. How many days was Gus’s car parked at the airport?

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