Question 1: If y is directly proportional to x and y = 10 when x = 5, find the constant of proportionality k.

Answer: 2

Question 2: Plot the graph of y = 3x for x values from 0 to 5.

Answer: Student draws the graph on the grid.

Question 3: Given the proportionality y ∝ x, if y = 20 when x = 4, what is the value of y when x = 7?

Answer: 35

Question 4: Construct a graph showing y = 5x and identify the point where y = 15.

Answer: At x=3, y=15.

Question 5: A car rental company charges $50 plus $0.20 per mile. Is the cost directly proportional to the miles driven? Explain your reasoning.

Answer: No, because of the fixed base charge of $50; it is not proportional to miles.

Question 6: The length of a rectangle is directly proportional to its width. If the length is 12 cm when the width is 4 cm, find the length when the width is 7 cm.

Answer: 21

Question 7: Plot the line y = 4x on the grid. What is the value of y when x = 6?

Answer: 24

Question 8: A worker's wages are directly proportional to the number of hours worked. If the wages are $120 for 8 hours, what are the wages for 12 hours?

Answer: $180

Question 9: Identify the mistake: A student plots the graph y = 2x + 5 to represent a proportional relationship. Explain and correct the error.

Answer: The '+5' is an addition, not consistent with direct proportion. Correct graph: y = 2x.

Question 10: In a recipe, the amount of sugar is directly proportional to the number of servings. If 100g of sugar is needed for 4 servings, how much is needed for 10 servings?

Answer: 250g

Question 11: Challenge: The graph of y = kx passes through points (2, 10) and (5, 25). Find the value of k and write the equation of the line.

Answer: k=5; y=5x

Question 12: Estimate the value of y when x=8 on the graph of y=3x, and explain your reasoning.

Answer: y=24; since y=3x, when x=8, y=3*8=24.