Question 1: Given the equation y = 3x + 2, complete the table for x = -2, -1, 0, 1, 2.

Answer: {"x":[-2,-1,0,1,2],"y":[-4,-1,2,5,8]}

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

Answer: Points: (0,4), (1,3), (2,2), (3,1)

Question 3: Identify the error: The student plots y = 2x + 1 but uses y = 2x - 1 in their graph. Explain the mistake.

Answer: The student mixed up the y-intercept; they should have used +1, but plotted with -1.

Question 1: A line has the equation y = -2x + 5. Find the y-value when x = 4, and explain how the slope affects the growth of the line.

Answer: {"x":4,"y":-2}

Question 2: The teacher claims that the equation y = 0.5x + 1 has a positive slope. Is this correct? Justify your answer.

Answer: Yes, because the coefficient 0.5 is positive, indicating the line rises as x increases.

Question 3: A graph shows a line passing through (0, -3) and (2, 1). What is the slope? Show your working.

Answer: Slope m = (1 - (-3)) / (2 - 0) = 4/2 = 2.

Question 1: A car rental company charges a fixed fee of $50 plus $20 per day. Write the equation for the total cost y in terms of days x. If a customer rents a car for 5 days, how much will it cost? Show your work.

Answer: {"cost":150,"equation":"y = 20x + 50"}

Question 2: A gardener plants flowers along a path. The number of flowers = 10 per meter + 5. Write an equation for total flowers (y) based on meters (x). How many flowers are needed for a 7-meter path?

Answer: {"x":7,"y":75}

Question 1: Construct a line with slope -3 and y-intercept 4. Write the equation and plot the points for x = -1, 0, 1.

Answer: {"points":{"x":[-1,0,1],"y":[7,4,1]},"equation":"y = -3x + 4"}

Question 2: Identify and correct the mistake: A student says, 'Since y = 4x + 2, the line is horizontal.' Is this correct? Explain.

Answer: No, because a slope of 4 means the line rises steeply; a horizontal line has slope 0.

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

Answer: Points: (-2, -5), (0, -1), (2, 3)

Question 2: A line passes through (1, 4) and has a slope of -2. Write its equation.

Answer: y - 4 = -2(x - 1) => y = -2x + 6

Question 3: Identify the error: A student claims that because y = 5x + 0, the line passes through the origin. Is this true? Why or why not?

Answer: Yes, because the y-intercept c = 0, so the line passes through (0,0).