which line has a slope of 1/3and goes through (3, -1)?

Let's look at it like this: Do you the formula for any line (You might have heard it as slope-intercept form)?

Y = mx + c.

Where m is slope, and c is the vertical intercept.

y = (1/3)x + c.        Since it passes through (3, -1) it will satisfy the equation
                             x =3, y = -1

-1 = (1/3)*3 + c. 

-1 = 1 + c

-1 -1 = c

-2 = c

c = -2

y = (1/3)x -2.          Multiply through by 3

3*y = 3*(1/3)*x - 2*3

3y = 1x - 6

3y = x - 6