Slope-intercept form for a linear equation is written as y = mx + b, where m is the slope, which is calculated by taking the rise over the run between any two points on the line, and b is the y-intercept, which is the y-value when x is 0. The example given shows how to find the slope as rise/run = 4/2 = 2 and the y-intercept using the point (0, -4) to write the equation in slope-intercept form as y = 2x - 4.