Question 1: Choose three x-values that are equally spaced between -2 and 2. Calculate the corresponding y-values for the linear function y = 3x + 1, and tabulate your results.

Answer: x: -2, -1, 0; y: -5, -2, 1

Question 2: Plot the points for the function y = 2x on the grid using x-values of -3, 0, and 4. Write down the y-values you will plot.

Answer: x: -3, 0, 4; y: -6, 0, 8

Question 3: Explain why choosing x-values that are too close together might make plotting less efficient.

Answer: Choosing very close x-values results in many points, making plotting time-consuming, and small errors can have a bigger impact on the shape of the graph.

Question 4: Select four x-values for y = -x + 4 that will produce points spread out evenly on the graph. List your x-values and calculate the y-values.

Answer: x: -2, 0, 2, 4; y: 6, 4, 2, 0

Question 5: Given the function y = 0.5x - 1, choose x-values that will give y-values of -1, 0, and 1. Show your working.

Answer: x: 0, 2, 4

Question 6: A linear function has points at (1, 4), (3, 8), and (5, 12). Find the x-values for plotting the function using y-values 4, 8, and 12, and explain your choice.

Answer: x-values: 1, 3, 5; chosen to match known points for accurate plotting.

Question 7: Plot the points for y = -2x + 3 using x-values of -1, 0, and 2. Write down the y-values.

Answer: x: -1, 0, 2; y: 5, 3, -1

Question 8: Identify a common mistake students make when selecting x-values for plotting linear graphs and describe how to avoid it.

Answer: Choosing x-values that do not reflect the pattern of the function or are not spread out can lead to an inaccurate shape. To avoid this, select x-values that illustrate the trend clearly.

Question 9: Select x-values to plot y = 4x - 5, ensuring they cover a range that includes negative, zero, and positive values. Calculate the y-values.

Answer: x: -1, 0, 1, 2; y: -9, -5, -1, 3

Question 10: For the function y = 1.5x + 2, find x-values that produce y-values of 0, 3, and 6. Show your working.

Answer: x: -, 2, 4

Question 11: Challenge: For y = 2x + 1, if a student chooses only x-values of -10 and 10, what are the y-values? Do these x-values give a good representation of the function? Explain your reasoning.

Answer: y: -19, 21; These x-values show extreme points and may not effectively illustrate the linear trend; more varied x-values would be better.