the slope of the line that passes through the points (-6,w) and (-10,4) is 1/8. what is the value of w

Use the point-slope formula for the eqn of a str line:

y-k = m(x-h), where (h,k) is any point on the line.

Suppose we first focus on the given point (-10,4).  Let (h,k) = (-10,4).

Then  y-k = m(x-h) becomes    y-4 = m(x-[-10])

The other point is (-6,w), where w is the unknown we must determine.

w-4 = (1/8)(-6+10).  Find w:
 
Mult both sides by 8 to remove the fraction 1/8:

8w-32 = -6 + 10 = 4.  Then 8w = 32+4 = 36.  w = 36/8 = 4.5, or 9/2 (ans.)