Question 1: Given the graph of a line passing through (2, 3) and (4, 7), find the equation of the line in the form y=mx+c.

Answer: y=2x-1

Question 2: Plot the graph of y=3x+2 on the grid. (Note: You will need to draw the line based on the equation provided).

Answer: Correctly plotted line

Question 3: Construct a line passing through the point (1, 2) with a gradient of -0.5. Write its equation.

Answer: y=-0.5x+2.5

Question 4: A student claims that the line passing through (0, 4) and (2, 0) has an equation y=-2x+4. Is this correct? Identify and explain any mistake.

Answer: No, the correct equation is y=-2x+4. The student’s equation is correct, but the mistake is claiming the slope is positive when it is negative based on the points.

Question 5: From the graph, the line crosses the y-axis at y=5 and passes through (3, 2). What is the equation of this line?

Answer: y=-1x+5

Question 6: A line is drawn with an incorrect slope of 0.5 when the actual slope is -0.5. Describe how this mistake affects the derived equation and the graph.

Answer: Using a positive slope instead of negative results in a line with the wrong orientation, leading to an incorrect equation, e.g., y=0.5x+c, which would slope upwards instead of downwards.

Question 7: Given the points (1, 4) and (3, 8), find the equation and identify the mistake if a student gives y=2x+2.

Answer: Correct slope is 2. The mistake is in the intercept; the actual intercept is y=2x+2 is incorrect as the line passes through (1,4), which does not satisfy y=2x+2. The correct intercept is 2, so the equation y=2x+2 is correct, but students should verify the points.

Question 8: Identify and correct the error in this derivation: The line passing through (0, 1) and (2, 5) is given as y=2x+1.

Answer: The slope between the points is (5-1)/(2-0)=4/2=2, so the equation y=2x+1 is correct. No error exists in this derivation.

Question 9: A line with an equation y= -3x + c passes through (2, 4). Find the value of c and write the complete equation.

Answer: c=10, y=-3x+10

Question 10: Explain why a line passing through (1, 2) and (3, 6) cannot have the equation y=0.5x+1.

Answer: Because the actual slope between the points is (6-2)/(3-1)=4/2=2, not 0.5. The claimed equation has an incorrect slope, which does not match the points.