Exploring Direct & Inverse Variation: Graphing Challenges

1. A car travels at a constant speed. If the time taken to travel a distance is directly proportional to the distance, graph the relationship between time and distance for a speed of 60 km/h.

• The graph is a curve representing an exponential relationship.

• The graph is a straight line with a slope of 1/60, representing the relationship between time and distance.

• The graph shows a horizontal line indicating no change in time with distance.

• The graph is a straight line with a slope of 60.

2. The amount of gas consumed by a car is inversely proportional to the speed of the car. If a car consumes 10 liters of gas at 60 km/h, how much gas will it consume at 120 km/h? Graph this relationship.

• 15 liters

• 5 liters

• 12 liters

• 8 liters

3. A recipe requires 2 cups of flour to make 12 cookies. If the number of cookies is directly proportional to the amount of flour, how many cookies can be made with 5 cups of flour? Graph the relationship between flour and cookies.

• 30 cookies

• 36 cookies

• 18 cookies

• 24 cookies

4. The time it takes to complete a job is inversely proportional to the number of workers. If 4 workers can complete a job in 10 hours, how long will it take 8 workers? Graph the relationship between the number of workers and time.

• 5 hours

• 8 hours

• 12 hours

• 15 hours

5. The cost of apples is directly proportional to the weight. If 3 kg of apples cost $6, how much will 5 kg cost? Graph the cost versus weight relationship.

• $10

• $15

• $12

• $8

6. The volume of a gas is inversely proportional to the pressure applied. If a gas occupies 4 liters at 1 atmosphere of pressure, what will be its volume at 2 atmospheres? Graph the relationship between pressure and volume.

• 5 liters

• 3 liters

• 2 liters

• 1 liter

7. A plant grows directly proportional to the amount of sunlight it receives. If a plant grows 3 cm with 4 hours of sunlight, how much will it grow with 10 hours? Graph the growth against sunlight hours.

• 10 cm

• 7.5 cm

• 2 cm

• 5 cm

8. The speed of a boat is inversely proportional to the time it takes to travel a fixed distance. If it takes 5 hours to travel 100 km at a certain speed, how long will it take at double the speed? Graph the relationship between speed and time.

• 1 hour

• 10 hours

• 4 hours

• 2.5 hours

9. The number of pages printed is directly proportional to the time spent printing. If 50 pages are printed in 2 minutes, how many pages can be printed in 5 minutes? Graph the relationship between time and pages printed.

• 100 pages

• 150 pages

• 75 pages

• 125 pages

10. The intensity of light is inversely proportional to the square of the distance from the source. If the intensity is 100 lux at 1 meter, what is the intensity at 2 meters? Graph the relationship between distance and light intensity.

• 25 lux

• 200 lux

• 10 lux

• 50 lux