WHAT'S INCLUDED:

This lesson is aligned with §111.30. Grade 8, Middle School Advanced Mathematics, Adopted 2025.

• TEKS 8.2D. write and solve equations involving direct variation;

Task Card: 24 Questions:

1. The total cost y of buying bananas varies directly with the number of kilograms x purchased. If 6 kg costs $24, what is the cost for 8 kg?
   
2. In a chemistry experiment, the amount of gas released varies directly with the temperature. If 20 liters of gas is released at 40°C, how much gas is released at 60°C?
   
3. The number of pages a student can read varies directly with the number of hours spent reading. If a student reads 60 pages in 2 hours, how many pages can the student read in 6 hours?
   
4. The number of steps a robot takes is directly proportional to the time it runs. If the robot takes 1,400 steps in 20 minutes, how many steps does it take in 18 minutes?
   
5. A water tank is being filled at a constant rate. After 2 minutes, the tank has 16 liters of water. Assume direct variation. How many liters of water will the tank have after 8 minutes?
   
6. A recipe requires flour in direct proportion to the number of loaves of bread. If 16 cups of flour are used to bake 4 loaves, how much flour is needed for 10 loaves?
   
7. Talitha earns money by tutoring. She is paid $10 for every hour she tutors. What is the direct variation equation that represents the amount of money she earns for hours of tutoring?
   
8. A baker uses sugar in direct proportion to the number of cakes made. If 4 cakes need 8 cups of sugar, what is the direct variation equation relating the number of cakes to the amount of sugar?
   
9. A car travels at a constant speed. If the distance (d) traveled is directly proportional to the time (t) taken, which equation represents this relationship if the car travels 150 km in 3 hours?
   
10. A printing shop charges based on the number of pages printed. The rate is $0.12 per page. Let P be the price and n the number of pages. Which equation best describes the given situation?
    
11. A bike rental company rents out bikes for $7 per hour. Let R be the rental cost and h the number of hours rented. Which equation represents this direct variation?
    
12. A cyclist rides at a steady speed of 15 km/h. Let d be the distance in kilometers and t be the time in hours. Which equation represents this situation?
    
13. A table shows the relationship between x and y. Which equation represents the relationship between x and y?
    
14. A graph shows a straight line passing through the origin with a slope of 4. Which equation represents the relationship between x and y?
    
15. A table shows the relationship between the number of hours studied (x) and the score on a test (y). What is the equation that represents the direct variation between hours studied and test score?
    
16. A straight line passes through the origin and point (2, 4). What is the equation that represents the relationship between x and y as shown in the graph?
    
17. A table shows the relationship between the number of days (x) and the total cost (y) for renting a car. What is the equation that represents the direct variation between days and total cost?
    
18. A graph shows a line passing through the origin and the point (6, 18). The graph models the total distance y a person walks based on time x in hours. Which of the following equations best describes the relationship between time and distance?
    
19. A table shows the direct variation between the number of hours a machine operates and the number of units it produces. Based on the table, how many units will the machine produce in 10 hours?
    
20. A graph shows a straight line passing through the origin and the point (2, 50). The x-axis represents the number of boxes, and the y-axis represents the total cost in dollars. What is the cost per box?
    
21. The number of pages printed by a machine varies directly with the number of minutes it runs. How many pages will the machine print in 12 minutes?
    
22. A graph shows a direct variation between y and x. If the point (5, 25) lies on the graph, what is the equation of the line?
    
23. The distance traveled by a car varies directly with the time it travels at a constant speed. What distance will the car travel in 6 hours?
    
24. A graph shows a direct variation between time and total payment for a freelance job. The graph passes through (0, 0) and (1, 30). If a freelancer works for 8 hours, how much should they be paid?