Question 1: If y is directly proportional to x with a constant of proportionality 3, find y when x = 5.

Answer: 15

Question 2: Plot the graph of y = 4x for x values from 0 to 10. Use the grid to draw the line.

Answer: Graph plotted correctly showing y=4x from x=0 to x=10.

Question 3: Given y = 6x, what is the value of y when x = 7? Show your working.

Answer: 42

Question 4: A car travels at a speed proportional to the fuel used. If 8 liters of fuel allow it to travel 120 km, how far can it travel on 12 liters? Show your reasoning.

Answer: 180 km

Question 5: Complete the table for y = 2x: | x | y | |---|---| | 0 | ? | | 3 | ? | | 5 | ? | | 10 | ? |

Answer: 0, 6, 10, 20

Question 6: Explain why the graph of y = 5x is a straight line passing through the origin.

Answer: Because y is directly proportional to x with a constant of 5, resulting in a straight line through (0,0).

Question 7: If a bicycle’s speed is proportional to the effort applied, and applying effort 4 units results in a speed of 20 km/h, what effort is needed for a speed of 30 km/h?

Answer: 6

Question 8: Plot the line y = 3x on the grid for x values 0 to 8. Ensure the line is straight and passes through the origin.

Answer: Graph correctly showing y=3x from x=0 to x=8.

Question 9: A recipe uses ingredients in a ratio proportional to the number of servings. If 2 cups of sugar are used for 4 servings, how much sugar is needed for 10 servings?

Answer: 5

Question 10: Identify and correct the mistake in the statement: "Since y ∝ x, the graph of y = 2x is a parabola."

Answer: The graph of y=2x is a straight line, not a parabola.

Question 11: Challenge: The constant of proportionality varies with x. Is y still directly proportional to x? Explain.

Answer: No, because the proportionality constant is not constant; y is not directly proportional to x.