Both equations are lines with a slope of 2. They will be parallel. They differ only in their y-intercept.
It can work well to graph the y-intercept, then plot another point that is at some horizontal distance from the y-axis and twice that distance above the y-intercept.
y = 2x + 3
Plot the point (0, 3) and the point (2, 7). Draw a line through those points.
y = 2x - 2
Plot the point (0, -2) and the point (2, 2). Draw a line through those points.