Writing and Solving Linear Functions

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?