Question 1: Write the equation of a line with slope m=3 and y-intercept c=2.

Answer: y=3x+2

Question 2: Plot the line with equation y=–2x+4 on the graph paper provided.

Answer: Correctly plotted line showing y=–2x+4

Question 3: Calculate the y-value when x=5 for the line y=0.5x–1.

Answer: 1.5

Question 4: A line has slope m=–1 and passes through (0, 3). Write its equation.

Answer: y=–x+3

Question 1: Given a line with m=4 and c=–3, find the coordinates of the point where the line crosses the y-axis and plot the line.

Answer: Crosses y-axis at (0,–3); plotted line y=4x–3

Question 2: A line with equation y=2x+1 is shifted parallelly down by 3 units. Write the new equation and explain why the slope remains unchanged.

Answer: y=2x–2; slope unchanged because parallel shift does not affect slope

Question 3: Determine whether the line y=–0.5x+5 is increasing or decreasing. Justify your answer.

Answer: Decreasing, because slope m=–0.5 is negative

Question 4: A student claims that changing c in y=mx+c affects the slope of the line. Explain whether this statement is correct or not.

Answer: Incorrect; changing c shifts the line vertically but does not change the slope m

Question 1: A car rental company charges a flat fee of $20 plus $0.15 per mile. Write the equation for the total cost and identify m and c.

Answer: Cost = 0.15x + 20; m=0.15 (cost per mile), c=20 (flat fee)

Question 2: A water tank is filling such that the height h in cm increases at a rate of 0.8 cm per minute, starting from 10 cm. Write the equation describing height over time t (in minutes).

Answer: h=0.8t+10

Question 1: Construct a line with slope m=–3 that passes through the point (2, 5). Write its equation and plot it on the grid.

Answer: y=–3x+11

Question 2: Explain why two lines with the same slope but different c values are parallel, and illustrate with an example.

Answer: Lines y=2x+1 and y=2x–4 are parallel because they have the same slope m=2 but different y-intercepts

Question 1: A student writes the equation y=–4x+ c but mistakenly believes that changing c affects the slope. Identify the mistake and correct the statement.

Answer: Mistake: c affects the y-intercept, not the slope. Correct statement: changing c shifts the line vertically without changing slope.

Question 2: A line with slope 0.5 is incorrectly described as decreasing. Is this correct? If not, explain.

Answer: Incorrect; slope 0.5 is positive, so the line is increasing, not decreasing.