Okay, so the equation for the y-intercept is y=mx+b, this will be your base for graphing anything.
For y = x + 3 it's basically y = 1x + 3. Use b as the y-intercept, or 3, and plot it as (x,y), (0,3). Then use m as the slope, or 1. 1 means positive one so the point goes (0,3), (1, 4), (2, 5).
For y = -3x - 1 it's the same thing but different numbers. Use b, the y-intercept, and plot it. -1 is b, so plot (0,-1). Then use the slope to go up or down the direction you need to go, or m. m is -3, so for every +1 in x, the y will decrease by 3. (0,-1), (0,-4), (0,-7).
I hope this helped in some way or increased your understanding!