WHAT'S INCLUDED:

• Google Classroom
• Task Card
• 6 Jobs/ Professions where this Math is used or can be used.

This lesson is aligned with TEKS - Algebra 1

• A.2D: Write and solve equations involving direct variation.

1. In the equation y = kx, what does k represent?
   
2. Which situation represents a direct variation?
   
3. Which graph represents a direct variation?
   
4. Which of the following is not an example of direct variation?
   
5. Verify the statement: “The equation y = 2x + 5 represents a direct variation.”
   
6. The graph represents a direct variation.
   
7. The line graph below shows a direct relationship between time and distance. After 2 hours, a cyclist travels 60 km. What is the distance after 5 hours?
   
8. The table below models a direct variation. Write an equation for this relationship.
   
9. The amount of money earned on a job is directly proportional to the number of hours worked. If $70.00 is earned in 5 hours, how much money is earned in 20 hours of work?
   
10. A recipe uses 2 cups of flour for 4 cookies. How much flour is needed for 10 cookies?
    
11. The table below shows the recorded distance of a runner over time. The data models a direct variation. How far will the runner run in 4 hours at the same rate?
    
12. The graph shows the distance traveled over time. What is the constant of variation (rate of travel) shown in the graph?
    
13. Two workers are paid based on direct variation: Worker A earns $12/hour, Worker B earns $18/hour. Who earns more after 10 hours and why?
    
14. If y varies directly with x and y = 24 when x = 6, what will y be when x = 12?
    
15. You notice that as x increases by 2, y increases by 10. What is the constant of variation in this direct relationship?
    
16. The fruit seller says, “Buy 5 kg of watermelon for $20.” What assumption must be true for this to reflect direct variation?
    
17. You are shown two receipts. Are both purchases priced at the same rate?
    
18. A student writes: “If y = 12 when x = 3, then the direct variation is y = 3x.” What is the error of the solution?
    
19. A nurse calculates a patient’s IV drip rate. For every 1 hour, 60 mL of fluid is delivered. What is the equation for the total fluid F delivered after h hours?
    
20. A recipe uses 3 cups of rice to serve 6 people. A chef needs to serve 20 guests. How much rice should they use?
    
21. A data analyst finds that a store's revenue increases by $2,000 for every 100 units sold. What is the equation for revenue R based on units sold u?
    
22. A software engineer creates a server load planning through a table. How many processors are needed to support 1,000 users, assuming a direct variation?
    
23. A Veterinarian’s dosage medication of a dog is shown in the graph. What is the correct equation that models the graph and determine the dosage for a 35-pound dog?
    
24. An electrician charges based on direct variation. What equation models their rate, and how does this relate to time management?