Question 1: Calculate the y-values when x = -2, 0, 3 for the linear function y = 2x + 1.

Answer: y = -3, 1, 7

Question 2: If the table shows x-values 1, 2, 4, 8, explain whether these are suitable x-values for plotting y = 3x + 2. Justify your answer.

Answer: Yes, these x-values are suitable because they cover a range around zero and increase systematically, allowing a clear graph.

Question 3: Plot the points for x = -3, 0, 3 on the grid for y = -x + 4.

Answer: Points: (-3, 7), (0, 4), (3, 1)

Question 4: Construct a table of x and y values for y = 4 - 2x, choosing x-values at -2, 0, 2, 4.

Answer: x: -2, 0, 2, 4; y: 8, 4, 0, -4

Question 1: A linear function y = 5x + k passes through the point (2, 13). Find the value of k and suggest three x-values that would be suitable for plotting this function.

Answer: k=3; suitable x-values: -1, 0, 3

Question 2: Explain why choosing x = 0, 1, 2 might be problematic when plotting y = 0.5x^2. Suggest better choices.

Answer: Because x = 0, 1, 2 are close together and do not show the curvature well; better choices are x = -2, 0, 3 for better curve visualization.

Question 3: Given y = -2x + 5, explain the importance of choosing x-values that are both positive and negative when drawing the graph.

Answer: Choosing both positive and negative x-values helps visualize the entire linear relationship, including intercepts and slope direction.

Question 1: A mobile phone plan charges a fixed fee plus a cost per minute. The total cost y depends on the number of minutes x. If y = 20 + 0.10x and the customer used 50 minutes, which x-values should they choose to plot to see the cost increase? Why?

Answer: x-values: 0, 25, 50, 75; chosen to show how costs increase with minutes, including zero minutes.

Question 2: A company's profit y depends on advertising x, where y = 4x - 10. Which x-values would give the most insight into profit behavior? Justify your choice.

Answer: x-values: 0, 2, 5, 10; to see the influence of advertising on profit, including zero and higher values.

Question 1: For y = 2x + 3, find x-values between -5 and 5 that will produce y-values at least 0. Explain your reasoning.

Answer: x ≥ -1; x-values: -1, 0, 1, 2, 3, 4, 5

Question 2: Identify and correct the mistake in selecting x-values -3, 0, 3 when plotting y = -x^2 + 4x. Why is this mistake significant?

Answer: Mistake: neglecting negative x-values; correction: include x = -2 to observe the parabola's shape properly.

Question 1: Choose x-values that would help plot y = 3x - 1 to clearly show the line's slope and intercept. Justify your choices.

Answer: x = -2, 0, 2; these span negative, zero, and positive x-values to demonstrate slope and intercept.

Question 2: If a student picks only x = 1, 2, 3 for y = 4x + 2, what misconception might they have?

Answer: They might think only these points are enough to plot the line, missing the importance of a broader range.