To understand different types of linear equations by looking at their graphs, focus on these key points:

1. Slope:

   • The slope tells us how steep the line is.
   • A positive slope (when it goes up) means the line rises from the left side to the right side.
   • A negative slope (when it goes down) means the line falls from left to right.

2. Y-intercept:

   • This is where the line meets the y-axis (the vertical line on a graph).
   • You can find it in the equation $y = mx + b$: the $b$ stands for the y-intercept.

3. Types of Lines:

   • Horizontal Lines:
     • They look like a flat line and can be written as $y = c$ (for example, $y = 3$).
     • They have a slope of 0.
   • Vertical Lines:
     • These lines go straight up and down and are written as $x = c$.
     • They have an undefined slope, which means we can’t really talk about steepness.

4. Graph Characteristics:

   • Parallel Lines:
     • These lines never cross each other.
     • They have the same slope but different y-intercepts.
   • Intersecting Lines:
     • If two lines cross, it means they have different slopes.
     • This creates a unique point where they meet, showing there is a solution.

By recognizing these features, it's easier to tell apart linear equations when looking at their graphs.