Question 1: Recall the formula for calculating the gradient (slope) between two points on a graph: m = (change in y) / (change in x). A positive gradient indicates the line rises from left to right.

Answer:

Question 1: Calculate the gradient of the line passing through points (2, 3) and (5, 7).

Answer: 4/3

Question 2: Determine whether the gradient between (1, 2) and (4, 5) is positive, negative, or zero.

Answer: positive

Question 3: Plot the graph of y = 2x for x values from 0 to 3. Describe the gradient of this line.

Answer: The gradient is 2, and it is positive.

Question 1: A student claims that a line with a positive slope must always pass through the origin. Is this true? Explain your answer.

Answer: No, a line with a positive slope does not have to pass through the origin.

Question 2: Identify the mistake: The student calculates the gradient between points (1, 2) and (1, 5) as positive. Is this correct? Why or why not?

Answer: No, because the change in x is zero, so the gradient is undefined, not positive.

Question 1: A car travels along a straight road. Its distance from a starting point (in km) over time (in hours) is represented by the graph. The line from 0 to 3 hours has a gradient of 3 km/hour. What does this tell you about the car's movement? Is the gradient positive? Why?

Answer: The positive gradient indicates the car is moving away from the start at 3 km/hour.

Question 2: Given points (2, 4) and (6, 10), find the gradient and explain whether it is positive or negative. What does this indicate about the line?

Answer: Gradient = (10-4)/(6-2) = 6/4 = 3/2, which is positive, indicating the line rises from left to right.

Question 1: A graph shows the growth of a plant over days. The line between days 1 and 5 has a gradient of 2 cm/day. Is the plant growing positively? Explain.

Answer: Yes, the positive gradient indicates the plant is growing each day.

Question 1: Construct a line on the grid with a positive gradient of 3/4 passing through (2, 3). Write the equation of this line.

Answer: y - 3 = (3/4)(x - 2) or y = (3/4)x + 1.5

Question 2: If a line has a positive gradient but passes through the point (0, -2), what is its equation if the gradient is 5/2?

Answer: y + 2 = (5/2)x or y = (5/2)x - 2

Question 1: True or False: All lines with positive gradients pass through the origin.

Answer: False

Question 2: A line with a gradient of 0 is horizontal. Is its gradient positive? Why or why not?

Answer: No, because a gradient of 0 is neither positive nor negative.