Get the equation into slope-intercept form y= mx + b
y = x + 3
This tells you that when x = 0, y = 3, plot the point (0, 3) on the graph.
No calculation involved. The answer is right there in front of you, b is the y-intercept.
Armed with this information you can proceed one of two ways.
Calculate another point. If x = 1, then the equation is
y = (1) + 3 = 4
so the point (1,4) is also on the line, plot (1,4) and draw the line that connects it with (0,3)
The slope (m in the equation) is one, so count over 1 unit to the right from (0, 3) and then one unit up to point (1, 4), plot it and draw the line that connects the two points.
Had the slope been -1 you would count one to the right and one down.
Has the slope been 2, you would have counted one to the right and up two.
Had the slope been 1/2, you would count over two to the right and up one.