Two lines are parallel if the have the same slope. To find the slope of the line parallel to the line y=4/7x-2 we need to get the line into slope-intercept form (y = mx + b), but the line is already in that form, so the slope is m = 4/7.
Because two lines are parallel if the have the same slope, we concluded that the slope of the parallel to y=4/7x-2 is m = 4/7.