Question 1: Choose x-values of 0, 2, and 4, and calculate their corresponding y-values for the linear equation y=3x+1. Record your answers.

Answer: x=0, y=1; x=2, y=7; x=4, y=13

Question 2: For the equation y=−2x+5, if x=1, what is y? Show your calculation.

Answer: y=3

Question 3: Plot the points for x-values 0, 1, 2, 3 in the table below for y=4x−2. (Use the grid provided.)

Answer: x=0, y=−2; x=1, y=2; x=2, y=6; x=3, y=10

Question 4: Select x-values that will produce y-values between 0 and 10 for y=2x+3. List three possible x-values.

Answer: x=−1, 0, 3

Question 5: If a student chooses x=−2, 0, and 2 for y=−x+4, what are the corresponding y-values?

Answer: x=−2, y=6; x=0, y=4; x=2, y=2

Question 6: Problem Solving: A line has the equation y=5x−3. If the y-value is 12, what x-value should be chosen? Show your working.

Answer: x=3

Question 7: Real-world Application: A car rental company charges a base fee plus 2 dollars per day. If total cost y is given by y=2x+20, where x is the number of days, choose x-values that result in total costs between $30 and $50. List three x-values.

Answer: x=5, 6, 7

Question 8: Construct a table for y=−x+8, choosing x-values from −2 to 2. Fill in the table.

Answer: x=−2, y=10; x=−1, y=9; x=0, y=8; x=1, y=7; x=2, y=6

Question 9: Challenge & Extension: Find x-values that produce y-values of 0, 3, and 7 in the equation y=−2x+4. Explain your method.

Answer: x=2, 0, −1

Question 10: Error Analysis: A student chooses x=1, 2, and 3 for y=3x−2, but records y-values as 1, 4, and 5. Identify and correct the mistake.

Answer: Incorrect y-values; correct y-values are 1, 4, 7