Question 1: Given the linear function y=3x, choose x-values from -2 to 2 and complete the table with the corresponding y-values.

Answer: {"x":[-2,-1,0,1,2],"y":[-6,-3,0,3,6]}

Question 2: Plot the points for y=2x+1 when x=-3, 0, and 4.

Answer: (-3, -5), (0, 1), (4, 9)

Question 3: Why are some x-values more suitable than others when plotting a linear graph? Provide two reasons.

Answer: Suitable x-values produce clear, well-spaced points; values should avoid large or awkward numbers to make plotting easier.

Question 4: Choose five x-values between -5 and 5 that will give a good, accurate graph of y= -x + 4.

Answer: x = -5, -2, 0, 2, 5

Question 5: Construct a table for y=0.5x - 2, choosing x-values from 0 to 8 at intervals of 2.

Answer: {"x":[0,2,4,6,8],"y":[-2,-1,0,1,2]}

Question 6: A linear function has points plotted at (1,3), (3,7), and (5,11). What is the most appropriate next x-value to extend the table and why?

Answer: x=7, because the pattern increases by 2 in x and 4 in y, maintaining the linear trend.

Question 7: Select x-values between -3 and 3 that will produce a smooth, continuous linear graph for y=4x - 1. Explain your choices.

Answer: x = -3, -1, 0, 1, 3; these are evenly spaced and produce clear points for plotting.

Question 8: Plot the points for y=0.5x + 2 when x=-4, 0, and 4. Then, explain how changing the x-values affects the shape of the graph.

Answer: Points: (-4, 0), (0, 2), (4, 4). Increasing x-values increases y linearly; choosing wider x-values extends the line further.

Question 9: A student chooses x-values of -10, 0, and 10 to plot y=3x + 2. Identify and correct any issues with these x-values for accurate graphing.

Answer: These x-values are valid; they span negative, zero, and positive points, providing a good range for the graph.

Question 10: For the function y = -2x + 5, choose x-values that will produce points with both positive and negative y-values. Justify your selection.

Answer: x = -2, 0, 3; because these produce y-values of 9, 5, and -1, covering positive and negative y-values.