patrick_caldwell
patrick_caldwell 5d ago • 0 views

Real-world examples of line of best fit interpolation (Grade 8)

Hey there! 👋 Ever wondered how we can guess values between known data points on a graph? 🤔 That's where line of best fit interpolation comes in handy! Let's explore some real-world examples and then test your knowledge with a quick quiz. Ready to learn? 🤓
🧮 Mathematics

1 Answers

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📚 Quick Study Guide

  • 📈 A line of best fit is a straight line that represents the trend of data points on a scatter plot.
  • 📏 Interpolation is the process of estimating a value within the range of known data points using the line of best fit.
  • ✏️ To interpolate, find the x-value on the line of best fit and read off the corresponding y-value.
  • ⚠️ Interpolation is most reliable when the data points are closely clustered around the line of best fit.
  • 🔢 The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

🧪 Practice Quiz

  1. A scientist collects data on the growth of a plant over several weeks and creates a scatter plot. The line of best fit shows that after 4 weeks, the plant is approximately 10 cm tall, and after 6 weeks, it's 15 cm tall. Using interpolation, what is the estimated height of the plant after 5 weeks?
    1. 7.5 cm
    2. 12.5 cm
    3. 13 cm
    4. 10 cm

  2. A store owner tracks the number of ice cream cones sold based on the daily high temperature. The line of best fit suggests that when the temperature is 70°F, 20 cones are sold, and when it's 80°F, 30 cones are sold. Approximately how many ice cream cones would be sold if the temperature is 75°F?
    1. 22
    2. 25
    3. 28
    4. 32

  3. A student records the number of hours they study for a test and their corresponding test scores. The line of best fit indicates that studying for 2 hours results in a score of 70, and studying for 4 hours results in a score of 80. What score can they expect if they study for 3 hours?
    1. 65
    2. 70
    3. 75
    4. 85

  4. A delivery company analyzes the time it takes to deliver packages based on the distance traveled. The line of best fit shows that it takes 30 minutes to deliver a package 10 miles away and 45 minutes to deliver a package 20 miles away. Using interpolation, how long would it take to deliver a package 15 miles away?
    1. 35 minutes
    2. 37.5 minutes
    3. 40 minutes
    4. 42.5 minutes

  5. A baker notes the relationship between the amount of sugar used in a recipe and the sweetness of the cake. The line of best fit indicates that using 1 cup of sugar results in a sweetness level of 6, and using 2 cups of sugar results in a sweetness level of 9. What is the estimated sweetness level if 1.5 cups of sugar are used?
    1. 6.5
    2. 7
    3. 7.5
    4. 8

  6. An athlete tracks their race times based on the number of weeks they train. The line of best fit shows that after 2 weeks of training, their time is 60 seconds, and after 4 weeks, their time is 55 seconds. What time can they expect after 3 weeks of training?
    1. 56.5 seconds
    2. 57.5 seconds
    3. 58 seconds
    4. 59 seconds

  7. A farmer records the yield of their crops based on the amount of fertilizer used. The line of best fit shows that using 5 kg of fertilizer results in a yield of 50 kg, and using 10 kg of fertilizer results in a yield of 75 kg. What yield can they expect if they use 7.5 kg of fertilizer?
    1. 55 kg
    2. 60 kg
    3. 62.5 kg
    4. 65 kg
Click to see Answers
  1. B
  2. B
  3. C
  4. B
  5. C
  6. B
  7. C

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