The points ( - 6,5) and ( - 7,q) fall on a line with a slope of 10. what is the value of q?

If you go on my profile you will see a similar problem that I already answered today.

Lets start by using a formula (don't remember the name) 

(y-y1)=M(x-x1)

M is slope and y is first y value and y1 is second y value same applies to X.

Substitute in the values.

(5-q) = 10(-6-(-7))

5-q = 10*(1)

5-q = 10

-q = 5

q = -5

Check:

Substitute in the value of "q" and use the formula to find slope:

(y1-y)/(x1-x)

Substitute 

(-5-5)/(-7-(-6))
-10/-1
10

Your  
The value of "q" is -5