Gradient describes the "steepness" of the line and is linked to the constant differences you studied in Numeric Patterns. Task 4.1: Trend Analysis [3 Marks] Categorize each line as Increasing, Decreasing, or Constant.

here are the solutions for the remaining tasks. Phase 4: Investigating Gradient (Rate of Change) [10 Marks] Task 4.1: Trend Analysis [3 Marks] | Equation | Trend | | :-------- | :-------- | | 1. y = (1)/(2)x + 2 | Increasing | | 2. y = 2x - 4 | Increasing | | 3. y = -2x + 2 | Decreasing | Task 4.2: Guided Discovery (Constant Difference) [4 Marks] Change in y: Step 1: From the table for Equation 2 (y = 2x - 4), select two consecutive x-values that differ by 1, for example, x=0 and x=1. When x=0, y = 2(0) - 4 = -4. When x=1, y = 2(1) - 4 = -2. Step 2: Calculate the difference in y-values. Change in y = y_x=1 - y_x=0 = -2 - (-4) Change in y = -2 + 4 Change in y = 2 Task 4.3: Connecting Equation to Slope [3 Marks] Observation: The "change in y" calculated in Task 4.2 is 2. The coefficient of x in the original equation y = 2x - 4 is also 2. This shows that the coefficient of x (the gradient) directly represents the constant change in y for every unit increase in x. Phase 5: Conclusion and Generalization [8 Marks] Task 5.1: The General Rule [3 Marks] The gradient (m) represents the steepness (or rate of change) of the line. The y-intercept (c) represents the point where the line crosses the y-axis (or the value of y when x is 0) of the line. The x-intercept is found by setting y to 0. Drop the next question!