SOLUTION: Find a linear function h such that h(-1)=-5 and h(7)=-6. What is h(3/2)?

First you interpret it as this problems:

Find the equation of the line that passes through the two points
(-1,-5) and (7,-6).  

Use the slope formula: 


     y2 - y1      (-6) - (-5)      -6 + 5     -1 
m = ---------- = -------------- = -------- = ----- = 
     x2 - x1        7 - (-1)        7 + 1      8

Then use the point-slope formula:

y - y1 = m(x - x1)

y - (-5) = (x - (-1) )

   y + 5 = (x + 1)

   y + 5 = x - 

       y = x -  - 5

       y = x -  - 

       y = x - 

Now replace y by h(x)
 
    h(x) = x - 

That's the first part.

What is h()?

Substitute  for x in

    h(x) = x - 

    h() =  - 

    h() =  -  

    h() =  - 

    h() =   
  
Edwin