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.

$$
\text{Change in y} = y_{x=1} - y_{x=0} = -2 - (-4)
$$
$$
\text{Change in y} = -2 + 4
$$
$$
\text{Change in y} = \boxed{2}
$$

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.