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This video explains why equations for lines on graphs are typically written in the form of y = mx + c for convenience and ease of comparison. The equation y = 2x + 3 is used as an example, where m represents the gradient and c is the y-intercept. In this case, m is 2, indicating the steepness of the line, and c is 3, showing where the line crosses the y-axis. By using this standardized form, it becomes simpler to visualize and draw the lines on a graph based on their gradient and y-intercept.