Graphing linear equations is a great way to see solutions clearly. When we use the standard form, which looks like $ax + b = 0$, we can understand it better. Here are some important benefits of this method:

1. Finding Solutions: The x-intercept is the point where the graph crosses the x-axis (this is where $y = 0$). This point shows us the solution to the equation.

2. Seeing Connections: The slope ($m$) and y-intercept ($c$) help us see how changes in $x$ change $y$. This makes it easier to understand the relationship between them.

3. Comparing Equations: When we graph several linear equations at once, we can find where they intersect. These intersection points show us the solutions they have in common.

In conclusion, using graphs to visualize linear equations helps us understand important ideas that are key for GCSE Mathematics.