To graph the linear equation y = 3x - 2, start by finding the y-intercept by setting x to zero, resulting in the point (0, -2). Next, determine the x-intercept by setting y to zero, which gives the point (2/3, 0). With these two points identified, plot them on the graph and connect them with a straight line. The slope of 3 indicates that the line will rise as it moves from left to right. This method effectively illustrates the linear relationship defined by the equation.