The slope will be the number that always sits next to x. So the slope in this case is 3/1. Which is rise over run. If it was a fraction, like 1/3, that would mean that the slope is rise one, run three.
If you want to find the y-intercept, you do that by putting a zero in for x, so you want to find the point that the line intersects the y-axis. So x would be zero, and wherever that point is is the y-intercept. In this case:
y = 3x - 1
y = 3(0) - 1
3 times 0 is zero
y = - 1 So, the y-intercept is - 1, or (0,-1)
To sketch the graph, you just place any number in for x or y (x is easier in this case), and solve it.
For example, I am going to say that x equals two.
y = 3(2)-1
y = 6-1
y = 5
So, your point to put on the graph would be (2,5) (x,y)