7th Grade 2nd 6 Weeks Strength Training math worksheet featuring graphing, equations, and problem-solving exercises.
7th Grade 2nd 6 Weeks Strength Training worksheet with math problems involving graphs, equations, and word problems.
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Step-by-step solution for: Constant Rate of Change (7.4) Strength Training Practice
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Show Answer Key & Explanations
Step-by-step solution for: Constant Rate of Change (7.4) Strength Training Practice
1. The graph shows a proportional relationship because it is a straight line passing through the origin (0,0). This means the ratio of y to x is constant for all points on the line.
2. The unit rate is 3 miles per hour. This is found by calculating the slope of the line: rise/run = 6 miles / 2 hours = 3 miles/hour.
3. The equation is y = 3x, where y represents miles and x represents hours.
4. To find the distance traveled in 5 hours, substitute x = 5 into the equation: y = 3 * 5 = 15 miles.
5. The constant of proportionality is 3, which represents the speed in miles per hour.
6. The point (4, 12) means that after 4 hours, the person has traveled 12 miles.
7. The point (0, 0) means that at the start (0 hours), the distance traveled is 0 miles.
8. The graph represents a proportional relationship because it is a straight line through the origin, indicating a constant rate of change.
9. The unit rate is 4 dollars per item, calculated as 8 dollars / 2 items = 4 dollars/item.
10. The equation is y = 4x, where y is cost in dollars and x is the number of items.
11. For 6 items, the cost is y = 4 * 6 = 24 dollars.
12. The constant of proportionality is 4, representing the cost per item.
13. The point (3, 12) means that 3 items cost 12 dollars.
14. The point (0, 0) means that 0 items cost 0 dollars.
15. The graph represents a proportional relationship because it is a straight line through the origin.
16. The unit rate is 2 gallons per minute, calculated as 4 gallons / 2 minutes = 2 gallons/minute.
17. The equation is y = 2x, where y is gallons and x is minutes.
18. In 7 minutes, y = 2 * 7 = 14 gallons are filled.
19. The constant of proportionality is 2, representing the fill rate in gallons per minute.
20. The point (5, 10) means that after 5 minutes, 10 gallons have been filled.
21. The point (0, 0) means that at time zero, 0 gallons have been filled.
22. The graph represents a proportional relationship because it is a straight line through the origin.
23. The unit rate is 5 pages per hour, calculated as 10 pages / 2 hours = 5 pages/hour.
24. The equation is y = 5x, where y is pages and x is hours.
25. In 4 hours, y = 5 * 4 = 20 pages are read.
26. The constant of proportionality is 5, representing the reading rate in pages per hour.
27. The point (3, 15) means that after 3 hours, 15 pages have been read.
28. The point (0, 0) means that at the start (0 hours), 0 pages have been read.
29. The graph represents a proportional relationship because it is a straight line through the origin.
30. The unit rate is 1.5 cups of flour per cup of sugar, calculated as 3 cups flour / 2 cups sugar = 1.5.
31. The equation is y = 1.5x, where y is cups of flour and x is cups of sugar.
32. For 8 cups of sugar, y = 1.5 * 8 = 12 cups of flour are needed.
33. The constant of proportionality is 1.5, representing the ratio of flour to sugar.
34. The point (4, 6) means that for 4 cups of sugar, 6 cups of flour are needed.
35. The point (0, 0) means that with 0 cups of sugar, 0 cups of flour are needed.
36. The graph represents a proportional relationship because it is a straight line through the origin.
37. The unit rate is 0.25 pounds per dollar, calculated as 1 pound / 4 dollars = 0.25.
38. The equation is y = 0.25x, where y is pounds and x is dollars.
39. For $12, y = 0.25 * 12 = 3 pounds can be bought.
40. The constant of proportionality is 0.25, representing the amount of candy per dollar.
41. The point (8, 2) means that for $8, 2 pounds of candy can be bought.
42. The point (0, 0) means that for $0, 0 pounds of candy can be bought.
43. The graph represents a proportional relationship because it is a straight line through the origin.
44. The unit rate is 10 miles per gallon, calculated as 30 miles / 3 gallons = 10 miles/gallon.
45. The equation is y = 10x, where y is miles and x is gallons.
46. With 7 gallons, y = 10 * 7 = 70 miles can be driven.
47. The constant of proportionality is 10, representing the car's fuel efficiency in miles per gallon.
48. The point (5, 50) means that with 5 gallons of gas, the car can drive 50 miles.
49. The point (0, 0) means that with 0 gallons of gas, the car can drive 0 miles.
50. The graph represents a proportional relationship because it is a straight line through the origin.
2. The unit rate is 3 miles per hour. This is found by calculating the slope of the line: rise/run = 6 miles / 2 hours = 3 miles/hour.
3. The equation is y = 3x, where y represents miles and x represents hours.
4. To find the distance traveled in 5 hours, substitute x = 5 into the equation: y = 3 * 5 = 15 miles.
5. The constant of proportionality is 3, which represents the speed in miles per hour.
6. The point (4, 12) means that after 4 hours, the person has traveled 12 miles.
7. The point (0, 0) means that at the start (0 hours), the distance traveled is 0 miles.
8. The graph represents a proportional relationship because it is a straight line through the origin, indicating a constant rate of change.
9. The unit rate is 4 dollars per item, calculated as 8 dollars / 2 items = 4 dollars/item.
10. The equation is y = 4x, where y is cost in dollars and x is the number of items.
11. For 6 items, the cost is y = 4 * 6 = 24 dollars.
12. The constant of proportionality is 4, representing the cost per item.
13. The point (3, 12) means that 3 items cost 12 dollars.
14. The point (0, 0) means that 0 items cost 0 dollars.
15. The graph represents a proportional relationship because it is a straight line through the origin.
16. The unit rate is 2 gallons per minute, calculated as 4 gallons / 2 minutes = 2 gallons/minute.
17. The equation is y = 2x, where y is gallons and x is minutes.
18. In 7 minutes, y = 2 * 7 = 14 gallons are filled.
19. The constant of proportionality is 2, representing the fill rate in gallons per minute.
20. The point (5, 10) means that after 5 minutes, 10 gallons have been filled.
21. The point (0, 0) means that at time zero, 0 gallons have been filled.
22. The graph represents a proportional relationship because it is a straight line through the origin.
23. The unit rate is 5 pages per hour, calculated as 10 pages / 2 hours = 5 pages/hour.
24. The equation is y = 5x, where y is pages and x is hours.
25. In 4 hours, y = 5 * 4 = 20 pages are read.
26. The constant of proportionality is 5, representing the reading rate in pages per hour.
27. The point (3, 15) means that after 3 hours, 15 pages have been read.
28. The point (0, 0) means that at the start (0 hours), 0 pages have been read.
29. The graph represents a proportional relationship because it is a straight line through the origin.
30. The unit rate is 1.5 cups of flour per cup of sugar, calculated as 3 cups flour / 2 cups sugar = 1.5.
31. The equation is y = 1.5x, where y is cups of flour and x is cups of sugar.
32. For 8 cups of sugar, y = 1.5 * 8 = 12 cups of flour are needed.
33. The constant of proportionality is 1.5, representing the ratio of flour to sugar.
34. The point (4, 6) means that for 4 cups of sugar, 6 cups of flour are needed.
35. The point (0, 0) means that with 0 cups of sugar, 0 cups of flour are needed.
36. The graph represents a proportional relationship because it is a straight line through the origin.
37. The unit rate is 0.25 pounds per dollar, calculated as 1 pound / 4 dollars = 0.25.
38. The equation is y = 0.25x, where y is pounds and x is dollars.
39. For $12, y = 0.25 * 12 = 3 pounds can be bought.
40. The constant of proportionality is 0.25, representing the amount of candy per dollar.
41. The point (8, 2) means that for $8, 2 pounds of candy can be bought.
42. The point (0, 0) means that for $0, 0 pounds of candy can be bought.
43. The graph represents a proportional relationship because it is a straight line through the origin.
44. The unit rate is 10 miles per gallon, calculated as 30 miles / 3 gallons = 10 miles/gallon.
45. The equation is y = 10x, where y is miles and x is gallons.
46. With 7 gallons, y = 10 * 7 = 70 miles can be driven.
47. The constant of proportionality is 10, representing the car's fuel efficiency in miles per gallon.
48. The point (5, 50) means that with 5 gallons of gas, the car can drive 50 miles.
49. The point (0, 0) means that with 0 gallons of gas, the car can drive 0 miles.
50. The graph represents a proportional relationship because it is a straight line through the origin.
Parent Tip: Review the logic above to help your child master the concept of constant rate of change worksheet with answers.
