GCSE Maths - How to Find the Equation of a Straight Line (y = mx + c)

📚 Main Topics

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)
Finding the Y-Intercept
- Identify the point where the line crosses the y-axis to determine ( c ).
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.

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.

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

By following these steps, you can effectively find the equation of any straight line presented on a graph.