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Modeling Real-World Situations with Linear Equations

Explore real-world scenarios and learn how to model them using linear equations in slope-intercept form. Practice finding total costs and quantities based on given conditions.

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Modeling Real-World Situations with Linear Equations

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  1. Lesson 5.1 - 5.3Write Linear EquationsModel Real-World Situations Essential Question: How do you find the equation of a line?

  2. Modeling Real-World Situations • You can model a real-world situation that involves a constant rate of change with an equation in slope-intercept form.

  3. How do I model a real-world situation? • Identify what you know • Slope and y-intercept? • Slope and a point? • Two points? • Calculate what you need • Start by writing the equation in point-slope form. • Convert to slope-intercept form. • Evaluate the function

  4. Recording Studio A recording studio charges musicians an initial fee of $50 to record an album. Studio time costs an additional $35 per hour. • Write an equation that gives the total cost of an album as a function of studio time (in hours). • Find the total cost of recording an album that takes 10 hours of studio time.

  5. Gym Membership Your gym membership costs $33 per month after an initial membership fee. You paid a total of $228 after 6 months. Write an equation that gives the total cost as a function of the length of your gym membership (in months). Find the total cost after 9 months.

  6. Web Server The initial fee to have a website set up using a server is $48. It costs $44 per month to maintain the website. • Write an equation that gives the total cost of setting up and maintaining a website as a function of the number of months it is maintained. • Find the total cost of setting up and maintaining the website for 6 months.

  7. Refreshments Your school club is making cookies for an upcoming school dance. On the morning of the dance, your group makes 5 batches of dough that yield 7.5 dozen cookies. In the afternoon, your group makes 7 batches of dough that yields 10.5 dozen cookies. • Write an equation that gives the number of dozen cookies as a function of the number of batches made. • How many dozen cookies can be made from 12 batches of dough? • If 12 cookies are in a dozen, how many cookies will 12 batches make?

  8. Dance Academy A dance academy charges $20 to use the facility and $25 per hour of instruction. • Write an equation that gives the total cost to learn to dance at the academy as a function of hours of instruction. • Find the total cost of 2 hours of dance instruction.

  9. Stickers You are designing a sticker to advertise to your band. A company charges $225 for the first 1000 stickers and $80 for each additional 1000 stickers. Write an equation that gives the total cost (in dollars) of stickers as a function of the number (in thousands) of stickers ordered. Find the cost of 9000 stickers.

  10. Advertising A radio station charges $650 for the first minute of ad time and then $340 for each additional minute. Write an equation that gives the total cost (in dollars) to run an ad as a function of the number of minutes the ad runs. Find the cost of 7 minutes of ad time.

  11. Working Ranch The table shows the cost of visiting a working ranch for one day and night for different numbers of people. If possible, write a linear equation that gives the cost as a function of the number of people in the group.

  12. Dog Boarding A dog kennel boards dogs for $8 a day. The kennel will also groom a dog for $12. • Write an equation that gives the total cost of lodging a dog and having it groomed once before it comes home as a function of the number of days the dog is at the kennel. • Find the total cost if you take your dog to the kennel for 5 days.

  13. Photographs A camera shop charges $3.99 for an enlargement of a photograph. Enlargements can be delivered for a charge of $1.49 per order. • Write an equation that gives the total cost of an order with delivery as a function of the number of enlargements. • Find the total cost of ordering 8 photograph enlargements with delivery.

  14. Aquarium Your family spends $30 for tickets to an aquarium and $3 per hour for parking. • Write an equation that gives the total cost of your family’s visit to the aquarium as a function of the number of hours that you are there. • Find the total cost of 4 hours at the aquarium.

  15. BMX Racing In Bicycle Moto Cross (BMX) racing, racers purchase a one year membership to a track. They also pay an entry fee for each race at that track. One racer paid a total of $125 after 5 races. A second racer paid a total of $170 after 8 races. How much does the track membership cost? What is the entry fee per race?

  16. Carnival Rides A carnival charges $2.50 per ride after an entrance fee. You paid a total of $22.50 after 6 rides. Write an equation that gives the total cost as a function of the number of rides. Find the total cost for 15 rides.

  17. How do you find the equation of a line given two points?

  18. Ticket Out the Door Write the equation of the line in slope-intercept form passing through the points and .

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