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

📚 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