Aline that includes the points (9,
-
6) and (v,
-
7) has a slope of
1

3
. what is the value of v?

Your numbers are all over the place, I will assume that you are saying that the slope is 13.

Looking at the formula for calculating slope/gradient, it is Rise/Run. 
Rise/Run = y2 - y1 divided by x2 - x1. The reason for this is because if you minus one y value from the other y value you get the difference in values which is the rise, and if you minus one x value from the other x value you get the difference in value  which is the run. 

So by using this formula, you get:
 
(7 - 6) / (v - 9) = 13
Therefore 1/(v - 9) = 13
If you multiply both sides by (v-9), you get 1= 13v - 117
you rearrange it to 13v = 118
If you divide by 13, you get your answer = 9.0769

You can check your answer by putting this value back into the gradient formula.
 
(7-6)/(9.0769-9) 
=13.004