Question 1: If y is directly proportional to x and y = 12 when x = 3, find the value of y when x = 7.

Answer: 28

Question 2: Plot the graph of y=4x for x values from 0 to 5. Draw the line on the grid.

Answer: Graph showing a straight line passing through (0,0) and (5,20).

Question 3: Construct a triangle with vertices at (0,0), (4,8), and (x,y). If y is proportional to x, find the coordinates of the third point when x=6.

Answer: (6,12)

Question 4: A car travels at a speed directly proportional to the time taken. If it covers 150 km in 3 hours, how far will it travel in 5 hours?

Answer: 250 km

Question 5: A student incorrectly assumes y ∝ x² instead of y ∝ x. Explain what mistake they are making and how it affects the graph.

Answer: They think y is proportional to x squared, so they plot a parabola instead of a straight line. This changes the shape and the nature of the relationship.

Question 6: Identify the mistake in the following statement: 'Since y is proportional to x, doubling x will double y.'

Answer: Correct; doubling x will double y because y ∝ x.

Question 7: In a table, when x = 2, y = 6; when x = 4, y = 12. Is y directly proportional to x? Justify your answer.

Answer: No, because the ratio y/x is not constant: 6/2=3, but 12/4=3, so yes, it is proportional.

Question 8: A graph shows a straight line passing through the origin with points (0,0) and (3,9). What is the constant of proportionality?

Answer: 3

Question 9: A common misconception is that y ∝ x² also appears as a straight line. Draw the graph of y=x² for x from -3 to 3 and explain why it’s not a straight line.

Answer: The graph of y=x² is a parabola, not a straight line, because y depends on x squared, which is nonlinear.

Question 10: Given the data points (1, 4), (2, 8), (3, 12), identify if they follow y ∝ x and justify your reasoning.

Answer: Yes, because y/x is constant: 4/1=4, 8/2=4, 12/3=4, indicating y ∝ x.

Question 11: Identify and correct the error in the following statement: 'If y ∝ x, then y/x = 0 when x = 0.'

Answer: Incorrect; y/x is undefined when x=0, so y cannot be proportional to x at x=0.

Question 12: Challenge Question: Suppose y ∝ x, and y = 5 when x=2. Find the value of y when x=10, and explain the steps involved.

Answer: First find the proportionality constant k: y= kx, so 5= k*2 → k=2.5. Then, y= 2.5*10=25.