Question 1: A scientist records the temperature at different times during an experiment. At time x=2 hours, the temperature is y=20°C. The temperature increases at a rate of 3°C per hour. Write the equation of the temperature line using y - y₁ = m(x - x₁).

Answer: y - 20 = 3(x - 2)

Question 2: Using the line equation from the previous question, what will be the temperature after 5 hours?

Answer: y=35°C

Question 3: Plot a line on the grid that passes through the point (1, 5) and has a gradient of 2.

Answer: y - 5 = 2(x - 1)

Question 4: A plant's growth is recorded over days. On day 3, the height is 15cm. The growth rate is 4cm per day. Write the equation of the growth line.

Answer: y - 15 = 4(x - 3)

Question 5: Identify the gradient and point in the equation y - 25 = 2(x - 7).

Answer: Gradient = 2, Point = (7,25)

Question 6: In an experiment, the temperature decreases at a rate of 1.5°C per hour, starting from 30°C at time x=0. Write the equation of the temperature line.

Answer: y - 30 = -1.5(x - 0) or y = -1.5x + 30

Question 7: A scientist measures the height of a substance over time. At 4 hours, the height is 10cm. If the height decreases by 0.5cm each hour, find the line equation.

Answer: y - 10 = -0.5(x - 4)

Question 8: A bacteria population grows following the line y - 200 = 50(x - 2). How many bacteria are there after 6 hours?

Answer: y=200 + 50(6-2)=200+200=400 bacteria

Question 9: Construct a line passing through (3, 12) with a gradient of -3. Write the equation.

Answer: y - 12 = -3(x - 3)

Question 10: A scientist observes that the pH level drops by 0.2 units per hour, starting from pH 7 at time zero. Write the equation of the pH level over time.

Answer: y - 7 = -0.2(x - 0) or y = -0.2x + 7

Question 11: Identify the common mistake: A student writes y - 10 = 2(x + 3) when given a point (3, 10) and gradient 2. Correct the mistake.

Answer: y - 10 = 2(x - 3)