The slope-intercept form of a linear equation is expressed as y = mx + b, where m represents the slope and b is the y-intercept. The slope indicates how steep the line is, showing the rate of change of y with respect to x. The y-intercept is the point where the line crosses the y-axis. This form is useful for quickly graphing linear equations. By identifying the slope and y-intercept, you can easily plot the line on a coordinate plane. The slope can be positive, negative, zero, or undefined, affecting the direction and steepness of the line.