You can show solutions to linear equations using a graph on the Cartesian plane. Here’s a simple guide on how this works:

1. Graphing the Equation:

   • Each linear equation can be written as (y = mx + b).
   • In this formula, (m) is the slope (how steep the line is), and (b) is the y-intercept (where the line crosses the y-axis).
   • This equation makes a straight line on the graph.

2. Where the Lines Cross:

   • The point where the line meets the x-axis is called the x-intercept. This happens when (y = 0).
   • The y-intercept is the point where the line crosses the y-axis (when (x = 0)).

3. Understanding Solutions:

   • Every place on the line, shown as ((x, y)), is a solution to the equation.
   • If two lines cross each other, the spot where they meet gives the solution to the system of equations.

4. Challenges for Students:

   • About 50% of Year 10 students find it hard to graph these lines.
   • This makes it easy to make mistakes when interpreting solutions.

By understanding these points, it becomes clearer how to work with linear equations on a graph!