The slope-intercept form of a linear equation is expressed as y = mx + b, where 'm' represents the slope (or steepness) of the line, and 'b' represents the y-intercept (the point where the line crosses the y-axis). This form is particularly useful because it allows for easy identification of both the slope and the y-intercept, making it straightforward to graph the line. The other forms mentioned, such as perpendicular and parallel forms, are used in specific contexts involving relationships between lines, while the standard form (Ax + By = C) does not explicitly show the slope and y-intercept, making it less convenient for this particular scenario.