📚 Main Topics

1. Equation of a LineUnderstanding the format ( y = mx + c )

   • ( m ): Gradient (slope) of the line
   • ( c ): Y-intercept (where the line crosses the y-axis)

2. Finding the Y-Intercept

   • Identify the point where the line crosses the y-axis to determine ( c ).

3. Calculating the Gradient

   • Use the formula: [\text{Gradient} (m) = \frac{\text{Change in } y}{\text{Change in } x}]
   • Select two points on the line to calculate the changes in y and x.

✨ Takeaways

• The equation of a line can be easily derived by identifying the y-intercept and calculating the gradient.
• The gradient can be visualized using a right-angled triangle formed by the changes in y and x between two points on the line.

🧠 Lessons

1. Identifying the Y-Intercept

   • Always start by finding the y-intercept ( c ) as it provides a straightforward value to plug into the equation.

2. Calculating the Gradient

   • Choose two clear points on the line to minimize errors in calculating the changes in y and x.
   • Remember that the gradient can be negative, indicating a downward slope.

3. Final Equation

   • Once ( m ) and ( c ) are determined, substitute them back into the equation format ( y = mx + c ) to get the final equation of the line.