Mastering Predictions and Y-Intercepts in Data Trends

A researcher collected data on the number of hours students study and their test scores. The line of best fit for the data is represented by the equation y = 5x + 60. What is the y-intercept of this line?

• 50

• 60

• 80

• 70

Using the same line of best fit from the previous question, predict the test score of a student who studies for 4 hours.

• 100

• 90

• [Predicted Score]

• 75

A car rental company found that the cost of renting a car can be modeled by the equation y = 20x + 50, where y is the total cost and x is the number of days rented. What is the y-intercept of this equation?

• 70

• 50x

• 50

• 20

Using the car rental company's equation, predict the total cost for renting a car for 7 days.

• $210

• $420

• $300

• $150

A farmer recorded the number of hours of sunlight and the yield of crops. The line of best fit is given by the equation y = 2.5x + 10. What does the y-intercept represent in this context?

• The y-intercept shows the total hours of sunlight needed for growth.

• The y-intercept represents the baseline crop yield of 10 when there are 0 hours of sunlight.

• The y-intercept represents the average yield per hour of sunlight.

• The y-intercept indicates the maximum crop yield possible.

Using the farmer's line of best fit, estimate the crop yield if the plants receive 6 hours of sunlight.

• Estimated crop yield is 25 bushels per acre.

• Estimated crop yield is 45 bushels per acre.

• Estimated crop yield is 30 bushels per acre.

• Estimated crop yield is 15 bushels per acre.

A gym tracks the number of members and the monthly revenue. The line of best fit is y = 150x + 200. What is the y-intercept, and what does it signify?

• 150

• 2000

• 100

• 200

If the gym continues to grow, predict the monthly revenue when there are 50 members.

• $1500

• $2000

• $2500

• $3000

A school analyzed the relationship between the number of extracurricular activities and student GPA. The line of best fit is y = 0.3x + 2. What is the y-intercept, and what does it indicate?

• The y-intercept is 3, indicating the GPA for a student with 1 extracurricular activity.

• The y-intercept is 2, indicating the maximum GPA a student can achieve.

• The y-intercept is 0, indicating no relationship between activities and GPA.

• The y-intercept is 2, indicating the expected GPA for a student with 0 extracurricular activities.

Using the school's line of best fit, predict the GPA of a student involved in 8 extracurricular activities.

• 3.5

• 2.8

• 4.0

• 3.0