Find a linear function h such that h(3)=7 and h(-1)= 14. what is h (1/2)?

As it is stated to be a linear function and you are given two points, you can make an equation of a line, in the form y = mx + b. 

To find the slope (m), the equation is (y2-y1) / (x2-x1). In this case, x1 = 3, y1 = 7, x2 = -1, and y2 = 14. 

So, we plug in these values into the equation to get (14 - 7)/(-1 - 3) = 7/-4 = -1.75. m = -1.75

Now to find the b value in the equation y = mx + b, we use the values we know and plug them into the equation. So,

7 = -1.75(3) + b
7 = -5.25 + b 
b = 12.25

Check if this works with the other equation: 

14 = -1.75(-1) + 12.25
= 1.75 + 12.25 = 14, checks out.

So, we know the function h is h(x) = -1.75 (x) + 12.25
We are asked to solve h(1/2), so simply plug it in for x. (I used 0.5 instead of 1/2 to make it simpler).

Doing this, we get
-1.75(0.5) + 12.25 = 11.375.

So, h (1/2) = 11.375

Hope this helps!